96 DS11 Abstracts IP0 Juergen Moser Lecture: The Many Facets of Chaos Chaos reveals itself differently in different situations. Un- derstanding its many aspects or facets will help in creating innovative models. My talk will illustrate how different facets of chaos lead us in different directions in my recent works on: HIV population dynamics; determining the current state of the atmosphere (for weather prediction); genome assembly (determining the sequence of ACGT’s for a species); partial control of chaos . James A. Yorke University of Maryland Departments of Math and Physics and IPST [email protected] IP1 Will the Climate Change Mathematics? Computational models of the Earth system lie at the heart of modern climate science. Concerns about their predic- tions have been illegitimately used to undercut the case that the climate is changing and this has put dynamical systems in an awkward position. It is important that we extricate ourselves from this situation as climate science, whose true objective is to build an understanding of how the climate works, badly needs our expertise. I will discuss ways that we, as a community, can contribute by highlight- ing some of the major outstanding questions that drive climate science, and I will outline their mathematical di- mensions. I will put a particular focus on the issue of si- multaneously handling the information coming from data and models. I will argue that this balancing act will im- pact the way in whch we formulate problems in dynamical systems. Christopher Jones University of North Carolina at Chapel Hill, USA & University of Warwick, United Kingdom [email protected] IP2 From Newton’s Cradle to New Materials The bouncing beads of Newton’s cradle fascinate children and executives alike, but their symmetric dance hides com- plex nonlinear dynamic behavior. Lift a bead on one side off a chain of a few suspended beads, let it swing back: one bead bounces off on the other side. Do the same with a long chain of beads: several beads bounce off on the other side. This represents an example of nonlinear wave dy- namics, which can be exploited for a variety of engineering applications. By assembling grains in crystals or layers in composites such that they support nonlinear waves, we are developing new materials and devices with unique proper- ties. We have constructed acoustic lenses that allow sound to travel as compact bullets that can be used in medical applications, have developed new materials for absorbing explosive blasts, and are exploring new ways to test air- craft wings and bone implants nondestructively with the help of nonlinear waves. Chiara Daraio Aeronautics and Applied Physics California Institute of Technology [email protected] IP3 How Can We Model the Regulation of Stress Hor- mones? Daily and monthly rhythms of hormones are well recog- nised. Less well known are the more rapid ultradian changes which are a characteristic of most biologically ac- tive hormone systems. We have looked at the regula- tion of the stress hormones glucocorticoids secreted by the adrenal glands. It has always been assumed that the episodic release of these hormones was a result of some form of pulse generator in the brain. A dispassionate look at this system however, revealed that there was a feed- forward:feedback relationship between the pituitary gland and the adrenal gland providing scope for a peripheral os- cillating hormonal system. The background to this system and the biological testing of our mathematical predictions will be described. Stafford Lightman University of Bristol, United Kingdom Staff[email protected] IP4 Climate Sensitivity, Feedback and Bifurcation: From Snowball Earths to the Runaway Greenhouse The concept of climate sensitivity lays at the heart of as- sessment of the magnitude of the imprint of human activi- ties on the Earth’s climate. Most commonly, the ”climate” is represented by a simple projection such as a global mean temperature, and we wish to know how this changes in re- sponse to changes in a single control parameter – usually atmospheric CO2 concentration. This problem is an in- stance of a broad class of related problems in parameter dependence of dynamical systems. I will discuss the short- comings of the traditional linear approach to this problem, particularly in light of the spurious ”runaway” states pro- duced when feedback becomes large. The extension to in- clude nonlinear effects relates in a straightforward way to bifurcation theory. I will discuss explicit examples arising from ice-albedo, water vapor, and cloud feedbacks. Finally, drawing on the logistic map as an example, I will discuss the problem of defining climate sensitivity for problems ex- hibiting structural instability. Raymond T. Pierrehumbert The University of Chicago Dept. of the Geophysical Sciences [email protected] IP5 Robust and Generic Dynamics: A Phenomenon/mechanism Correspondence If we consider that the mathematical formulation of natural phenomena always involves simplifications of the physical laws, real significance of a model may be accorded only to those properties that are robust under perturbations. In loose terms, robustness means that some main features of a dynamical system are shared by all nearby systems. In the talk, we will explain the structures related to the presence of robust phenomena and the universal mechanisms that lead to lack of robustness. Providing a conceptual frame- work, the goal is also to show how to provide a generic correspondence phenomenon/mechanism for all dynamical systems. Enrique Pujals
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96 DS11 Abstracts
IP0
Juergen Moser Lecture: The Many Facets of Chaos
Chaos reveals itself differently in different situations. Un-derstanding its many aspects or facets will help in creatinginnovative models. My talk will illustrate how differentfacets of chaos lead us in different directions in my recentworks on: HIV population dynamics; determining thecurrent state of the atmosphere (for weather prediction);genome assembly (determining the sequence of ACGT’s fora species); partial control of chaos .
James A. YorkeUniversity of MarylandDepartments of Math and Physics and [email protected]
IP1
Will the Climate Change Mathematics?
Computational models of the Earth system lie at the heartof modern climate science. Concerns about their predic-tions have been illegitimately used to undercut the casethat the climate is changing and this has put dynamicalsystems in an awkward position. It is important that weextricate ourselves from this situation as climate science,whose true objective is to build an understanding of howthe climate works, badly needs our expertise. I will discussways that we, as a community, can contribute by highlight-ing some of the major outstanding questions that driveclimate science, and I will outline their mathematical di-mensions. I will put a particular focus on the issue of si-multaneously handling the information coming from dataand models. I will argue that this balancing act will im-pact the way in whch we formulate problems in dynamicalsystems.
Christopher JonesUniversity of North Carolina at Chapel Hill, USA &University of Warwick, United [email protected]
IP2
From Newton’s Cradle to New Materials
The bouncing beads of Newton’s cradle fascinate childrenand executives alike, but their symmetric dance hides com-plex nonlinear dynamic behavior. Lift a bead on one sideoff a chain of a few suspended beads, let it swing back: onebead bounces off on the other side. Do the same with along chain of beads: several beads bounce off on the otherside. This represents an example of nonlinear wave dy-namics, which can be exploited for a variety of engineeringapplications. By assembling grains in crystals or layers incomposites such that they support nonlinear waves, we aredeveloping new materials and devices with unique proper-ties. We have constructed acoustic lenses that allow soundto travel as compact bullets that can be used in medicalapplications, have developed new materials for absorbingexplosive blasts, and are exploring new ways to test air-craft wings and bone implants nondestructively with thehelp of nonlinear waves.
Chiara DaraioAeronautics and Applied PhysicsCalifornia Institute of [email protected]
IP3
How Can We Model the Regulation of Stress Hor-mones?
Daily and monthly rhythms of hormones are well recog-nised. Less well known are the more rapid ultradianchanges which are a characteristic of most biologically ac-tive hormone systems. We have looked at the regula-tion of the stress hormones glucocorticoids secreted bythe adrenal glands. It has always been assumed that theepisodic release of these hormones was a result of someform of pulse generator in the brain. A dispassionate lookat this system however, revealed that there was a feed-forward:feedback relationship between the pituitary glandand the adrenal gland providing scope for a peripheral os-cillating hormonal system. The background to this systemand the biological testing of our mathematical predictionswill be described.
Stafford LightmanUniversity of Bristol, United [email protected]
IP4
Climate Sensitivity, Feedback and Bifurcation:From Snowball Earths to the Runaway Greenhouse
The concept of climate sensitivity lays at the heart of as-sessment of the magnitude of the imprint of human activi-ties on the Earth’s climate. Most commonly, the ”climate”is represented by a simple projection such as a global meantemperature, and we wish to know how this changes in re-sponse to changes in a single control parameter – usuallyatmospheric CO2 concentration. This problem is an in-stance of a broad class of related problems in parameterdependence of dynamical systems. I will discuss the short-comings of the traditional linear approach to this problem,particularly in light of the spurious ”runaway” states pro-duced when feedback becomes large. The extension to in-clude nonlinear effects relates in a straightforward way tobifurcation theory. I will discuss explicit examples arisingfrom ice-albedo, water vapor, and cloud feedbacks. Finally,drawing on the logistic map as an example, I will discussthe problem of defining climate sensitivity for problems ex-hibiting structural instability.
Raymond T. PierrehumbertThe University of ChicagoDept. of the Geophysical [email protected]
IP5
Robust and Generic Dynamics: APhenomenon/mechanism Correspondence
If we consider that the mathematical formulation of naturalphenomena always involves simplifications of the physicallaws, real significance of a model may be accorded only tothose properties that are robust under perturbations. Inloose terms, robustness means that some main features of adynamical system are shared by all nearby systems. In thetalk, we will explain the structures related to the presenceof robust phenomena and the universal mechanisms thatlead to lack of robustness. Providing a conceptual frame-work, the goal is also to show how to provide a genericcorrespondence phenomenon/mechanism for all dynamicalsystems.
Enrique Pujals
DS11 Abstracts 97
Instituto Nacional de Matematica Pura e Aplicada, [email protected]
IP6
Models and Control of Collective Spatio-TemporalPhenomena in Power Grids
We are asking modern power grids to serve under condi-tions it was not originally designed for. We also expect thegrids to be smart, in how they function, how they with-stand contingencies, respond to fluctuations in generationand load, and how the grids are controlled. To meet theseever increasing expectations requires extending power gridmodels beyond the scope of traditional power engineering.In this talk aimed at applied mathematicians and physi-cists I first review basics of power flows, and then outlinea number of new problems in modeling, optimization andcontrol theory for smart grids. In particular, I describe newapproaches to control of voltage and reactive flow in dis-tribution networks, algorithms to study distance to failure,and statistical analysis of cascading blackouts in transmis-sion networks.
Michael ChertkovLos Alamos National [email protected]
IP7
Pattern Formation and Partial Differential Equa-tions
The research I present is motivated by specific, but ubiqui-tous pattern in models from physics: Domain and wall pat-terns the magnetization forms in ferromagnets, the coars-ening of the phase distribution in demixing of polymerblends, the roughening of a crystal surface under depo-sition. Dynamically speaking, the type of models rangesfrom variational formulations, over (driven) gradient flowsto non-gradient systems. The challenge for a rigorous anal-ysis lies in the fact that we are interested in generic be-havior of solutions, as expressed by (experimentally andnumerically observed)scaling laws, that hold in the limit oflarge system sizes. We argue that methods from the theoryof partial differential equations can be used to provide atleast one-sided, optimal bounds on these scaling laws.
Felix OttoMax Planck Institute for Mathematics in the SciencesLeipzig, [email protected]
IP8
Mathematical Models for Tissue Engineering Ap-plications
The broad goal of tissue engineers is to grow functionaltissues and organs in the laboratory to replace those whichhave become defective through age, trauma, and diseaseand which can be used in drug screening applications. Toachieve this goal, tissue engineers aim to control accu-rately the biomechanical and biochemical environment ofthe growing tissue construct, in order to engineer tissueswith the desired composition, biomechanical and biochem-ical properties (in the sense that they mimic the in vivo tis-sue). The growth of biological tissue is a complex process,resulting from the interaction of numerous processes ondisparate spatio-temporal scales. Advances in the under-standing of tissue growth processes promise to improve the
viability and suitability of the resulting tissue constructs.In this talk, I highlight some of our recent mathematicalmodelling work that aims to provide insights into tissueengineering applications.
Sarah WatersUniversity of [email protected]
IP9
Moving Pattern Formation from the Real World tothe Lab, and the Reverse
This talk will describe three pattern formation experimentswhere natural systems were imported directly into the lab-oratory. The overall shape and subsequent rippling insta-bility of icicles is a complex free-boundary growth prob-lem. It has been linked theoretically to similar phenomenain stalactites. We grew laboratory icicles determined themotion of their ripples. Washboard road is the result ofthe instability of a flat granular surface under the actionof rolling wheels. The rippling of the road sets in above athreshold speed and leads to waves which travel down theroad. We studied these waves both in the laboratory andusing 2D molecular dynamics simulation. Columnar jointsare uncanny formations of ordered cracks in certain lavaflows. We studied these both in a lab analog system andin the field. Each of these three cases nicely illustrates thepleasures and pitfalls of such ”naturalistic” pattern forma-tion experiments. Collaborators: Antony Szu-Han Chen,Nicolas Taberlet, Jim McElwaine, Lucas Goehring and L.Mahadevan
Stephen MorrisUniversity of Toronto, [email protected]
CP1
Internal Lever Arm Model for Myosin II
Myosin II is a special type of enzyme, called motor protein,capable of transforming chemical energy into mechanicalwork. Among the many different approaches of the dif-ferent disciplines, one of the most commonly used is theenzyme kinetic approach, that uses a set of (arbitrary) dis-crete states, with different transition rate constants be-tween them. Here, we present a purely mechanical modelgiving a more realistic continuous pathway between the lo-cal equilibrium states of the molecule.
Andras BiboDepartment of Structural Mechanics,Budapest University of Tecnology and [email protected]
CP1
Modeling DNA Overstretching at the BasepairLevel
Many stretching experiments on single DNA molecules in-dicate that DNA initially overwinds when stretched, thenit unwinds and, at large forces, it undergoes a phase-transition indicated by a plateau on the force-displacementdiagrams. We utilize a discrete, basepair level model to in-vestigate the response of short DNA molecules to stretch-ing, taking into account the sequence dependent physicalproperties of DNA alongside with the coupling betweenthe step parameters. By constructing bifurcation diagramsof equilibrium configurations and studying the dependence
98 DS11 Abstracts
on basepair combinations we show that the discrete modelpredicts overwinding followed by unwinding as a result ofcoupling between modes of deformation, and that the over-stretching transition observed in our study is a result ofshear instability.
Attila G. KocsisDepartment of Structural MechanicsBudapest University of Technology and [email protected]
David SwigonDepartment of MathematicsUniversity of [email protected]
CP1
Geometric Mechanics of Molecules with Non-LocalInteractions
We derive equations of motion for the molecules exhibit-ing both local (elastic) and non-local (e.g. electrostaticor Lennard-Jones) interactions using a modified exact ge-ometric rods theory. We explicitly compute the equationswhen the charges positioned off the elastic backbone. Weshow that helices are exact stationary solutions of the re-sulting integro-differential equations, and that their linearstability can be analyzed exactly. Classification of helicalstates and their stability for realistic polymers is also pro-vided.
Vakhtang PutkaradzeColorado State [email protected]
CP2
Bifurcations in Models of Evolution of Polymor-phism
Biological processes that lead to polymorphism can be de-scribed using models of competing populations. The in-troduction of new competitors occurs on a timescale thatis long compared to the timescale of the population mod-els. To the extent that the dynamics on these timescalesdecouple, evolutionary models that describe polymorphicbranching can be interpreted as discrete dynamical systemswhose state space is the set of omega-limits of the under-lying population models. This talk develops this idea, andeffect of bifurcations in the population models on evolu-tionary outcomes.
Ernest BaranyNew Mexico State UniversityDept of Mathematical [email protected]
CP2
Cell Population Dynamics: Bifurcation Theory Re-veals Emergent Behaviour.
Quorum sensing, a biochemical mechanism enabling com-munication between unicellular microbes, allows emergenceof coordinated multicellular behaviour like synchronisationand change of state. An agent based model describing cel-lular metabolic states, based on Danino et. al (2010) ex-periments is derived and analysed. Numerical continuationuncovers possible emergent modes of coordination acrossvarying size populations in varying volume environment.
Mean field bifurcation analysis and large scale simulationsin BSim, a novel 3D simulation framework, validate theo-retical results.
Petros MinaDepartment of Engineering MathematicsUniversity of [email protected]
Mario Di BernardoUniversity of BristolDept of Engineering [email protected]
Krasimira Tsaneva-AtanasovaDepartment of Engineering MathematicsUniversity of [email protected]
Nigel SaveryUniversity of [email protected]
CP2
Dynamics of Infection Spreading in Adaptive Net-works with Communities
When an epidemic spreads in a population, individuals mayadaptively change the structure of their social contact net-work to reduce infection risk. Here we study the spread ofepidemics on an adaptive network with community struc-ture. We model the effect of heterogeneous communitieson infection levels and epidemic extinction. We show howan epidemic can alter the community structure. We alsostudy stochastic reintroduction of infection to a communitywhere the disease has died out.
Ilker TuncThe College of William and MaryApplied Science [email protected]
Leah ShawThe College of William & [email protected]
CP3
Synchronization of Degrade-and-fire Oscillations inSynthetic Gene Networks
In this talk, I will describe our recent experimental andtheoretical work on the synchronization of synthetic genenetworks exhibiting oscillatory gene expression within bac-terial cells. Recently, we constructed a synthetic two-geneoscillator based on delayed auto-repression, and observedrobust and tunable ”degrade-and-fire” oscillations in indi-vidual bacteria. Using a variant of the same design in whichthe feedback is mediated by a small molecule AHL, we wereable to observe synchronized gene expression oscillationsin a colony of bacteria within a microfluidic chamber. Inlarge systems, the collective oscillations formed propagat-ing spatiotemporal waves typical for reaction-diffusion sys-tems. I will introduce a theoretical model of the collectiveoscillations based on diffusively-coupled delay-differentialequations which allowed us to explain the observed phe-nomenology.
Lev S. Tsimring
DS11 Abstracts 99
University of California, San [email protected]
Tal Danino, Octavio [email protected], [email protected]
Jeff HastyDepartment of BioengineeringUniversity of California, San [email protected]
CP3
Cell Cycle Synchronization vs. Clustering
Motivated by experiments and theoretical work on respira-tory oscillations in yeast cultures, we study ordinary differ-ential equations models of cell-cycle systems with cell-cycledependent feedback. We assume very general forms of thefeedback and study the dynamics, particularly the cluster-ing behaviour of such systems.
Erik M. BoczkoDepartment of Biomedical InformaticsVanderbilt University Medical [email protected]
Bastien FernandezCentre de Physique [email protected]
Todd YoungOhio UniversityDepartment of [email protected]
Richard BuckalewUniversity of [email protected]
CP4
Dynamics in Modular Networks at the MesoscaleLevel
Modularity is one of the most important features that realnetworks exhibit since it greatly determines their function-ality. Although it is being analyzed from different view-points, it is not yet well understood the dynamical behaviorof modular networks at the mesoscale level. In this talk wepropose a technique to identify this behavior, presenting atheoretical justification of it and illustrating its validity bymeans of several applications.
Juan A. Almendral, Inmaculada LeyvaUniversity of Rey Juan CarlosMadrid, [email protected], [email protected]
Daqing LiDepartment of physicsBar Ilan [email protected]
Irene Sendina-NadalUniversity of Rey Juan Carlos, Madrid, [email protected]
Javier M. Buldu
Rey Juan Carlos [email protected]
Shlomo HavlinBar-Ilan [email protected]
Stefano [email protected]
CP4
Clustering of Networks with Mesoscaled StructureThrough Multilevel Networks
The concept of multilevel network has been introducedin order to embody some topological properties ofheterogeneous-type complex systems which are not com-pletely captured by the classical models. In this talk wewill focus on different approaches of clustering and the ana-lytical relationships between them. As main feature it willbe shown some analytical bounds among the clustering ofeach slice, the clastering of the projection network and theclustering of the whole multilevel network.
Regino Criado, Julio Flores, Alejandro Garcıa del Amo,Jesus Gomez-GardenesUniversidad Rey Juan [email protected], [email protected],[email protected],[email protected]
Miguel RomanceDepartamento de Matematica AplicadaUniversidad Rey Juan [email protected]
CP4
Communicability, Centrality and Communities inComplex Networks
The concept of communicability in complex networks ispresented. A general mathematical framework for definin-ing communicability functions is then introduced, whichgives rise to the use of matrix functions in networks. Wepresent a measure based on the exponential adjacency ma-trix of the network and extend this idea to the resolvent,pseudo-inverse of the Laplacian, Psi matrix functions andsome new matrix functions. The method is then illustratedfor the definition of centrality measures as well as for thedetection of communities in networks. For the last topica set of methods and algorithms are briefly presented andanalysed.
Ernesto EstradaUniversity of [email protected]
CP5
Vortex Generation by An Oscillatory Magnetic Ob-stacle
We consider the flow induced by oscillating magnets in aquiescent electrically conducting fluid. The motion of themagnets produces a periodic flow pattern that involves theinteraction of vortices created at different times of the cy-cle. As a result, hyperbolic and elliptic points are createdand conveyed within the flow. We propose a simple normal
100 DS11 Abstracts
form model for the flow, and show that it reproduces thebifurcations of flow patterns found numerically.
Morten BrønsTechnical University [email protected]
CP5
Optimal Harmonic Response in a ConfinedBodewadt Boundary Layer Flow
The Bodewadt boundary layer flow on the stationary bot-tom end wall of a finite rotating cylinder is very sensitiveto perturbations and noise. A comprehensive explorationof response to variations in the amplitude and frequencyof harmonic forcing reveils sharply delineated linear- andnonlinear-response regimes, with a sharp transition be-tween them at moderate amplitudes. Axisymmetric wavesalways decay to the steady basic state when the harmonicmodulation is suppressed, and the experimentally observedpersistent circular waves are not self-sustained.
Juan M. LopezArizona State UniversityDepartment of [email protected]
Younghae DoKyungpook National [email protected]
Francisco MarquesUniv. Polit‘ecnica de CatalunyaApplied [email protected]
CP5
Vortex Sheet Model for a Turbulent Mixing Layer
A vortex sheet model is used to study the evolution of avortex sheet in an Euler fluid. The equation of motion ofthe sheet is derived explicitly in closed form. The vortexsheet rolls up into a smooth double branched spiral in-stead of a chaotic cloud of point vortices. The problem ofspontaneous appearance of singularity in an evolving vor-tex sheet is partially suppressed by slight desingularizationof the sheet along arc length.
Ujjayan Paul, Roddam NarasimhaJawaharlal Nehru Centre for Advanced Scientific [email protected], [email protected]
CP6
Stability of Periodic-Wave Solutions in the Para-metrically Driven Damped Nonlinear SchroedingerEquation
This equation has two cn- and two dn-wave solutions. Ofthese, two solutions are proven to be unstable for all valuesof the driving and damping parameters, against perturba-tions periodic with the period of the wave. The third waveis unstable (to antiperiodic perturbations) when the forc-ing is weak and/or the period of the wave is large, butbecomes stable in the opposite limit. The stability proper-ties of the fourth periodic solution depend on the forcing
and the period in a complex way.
Igor Barashenkov, Maxim MolchanUniversity of Cape [email protected], [email protected]
CP6
Nonlinear Asymptotic Stability for a GeneralizedGierer-Meinhardt Model
This paper shows the nonlinear asymptotic stability in thesemi-strong interaction regime of N-pulses in a singularlyperturbed, weakly damped, reaction-diffusion system. Weprove results for a general nonlinearity that includes morespecific systems such as the Gierer-Meinhardt model. Weuse renormalization group techniques to prove nonlinearasymptotic stability. We achieve this by showing the eigen-value problem dichotomizes into a stable region near zeroand a smaller center region. We additionally show contrac-tive semigroup estimates.
Thomas BellskyMichigan State UniversityDepartment of [email protected]
Keith PromislowMichigan State [email protected]
CP6
Asymptotic Analysis of a Specific Type of Multi-Bump Blowup Solutions of the Ginzburg-LandauEquation
Via a geometric construction, two types of multi-bumpblowup solutions of the Ginzburg-Landau equation wereshown to exist previously. At ξ = 0, one type of the solu-tions is exponentially small, the other type is algebraicallysmall. Here, we use asymptotic methods to study the so-lutions which are algebraically small at ξ = 0. The keyingredient of the analysis is that the maximum of the solu-tions, the bump, must be placed at an essentially differentlocation than for the other type of solutions.
Vivi RottschaferLeiden UniversityDept of [email protected]
CP7
Some Effects of the Gamma Distribution on theDynamics of a Scalar Delay Differential Equation
We consider a scalar two-delay differential equation, con-sisting of one discrete and one gamma-distributed delay.We characterise the stability of the trivial solution as wellas the functional dependence of the stability regions ofthe Hopf bifurcation of this solution upon the parameterm ∈ Z+, the gamma distribution index.
Israel NcubeMemorial University of [email protected]
Sue Ann CampbellUniversity of WaterlooDept of Applied Mathematics
DS11 Abstracts 101
CP7
Periodic Orbits in Differential Equations withState-Dependent Delay
Delay-differential equations with a state-dependent delayare inherently nonlinear such that phenomena such as peri-odic orbits are possible and even likely. I show that periodicorbits are given as roots of a system of smooth algebraicequations. One immediate consequence of this is that thetechniques developed for the analysis of the Hopf bifurca-tion work as expected also in systems with state-dependentdelays.
Jan SieberUniversity of PortsmouthDept. of [email protected]
CP7
Cavitation in Tissue under High-Intensity FocusedUltrasound
Micro-bubbles occurring in tissue during heating of tu-mours by high-intensity focused ultrasound can enhance orinhibit treatment. Thus understanding of the oscillationsis essential. The bubbles are modelled as a system of cou-pled damped driven nonlinear oscillators, whose stabilityis investigated analytically and numerically. Tissue com-pressibility leads to a system of state dependent neutraldelay differential equations. It found that delays stabilisethe system, inhibiting many of the mechanisms which re-sult in unpredictable oscillations.
David Sinden, Eleanor Stride, Nader SaffariDepartment of Mechanical EngineeringUniversity College [email protected], [email protected], [email protected]
CP8
Computing N-Heteroclinic EtoP Orbits Near Non-Reversible Homoclinic Snaking
Non-reversible homoclinic snaking of a codimension-onehomoclinic orbit to an equilibrium is a phenomenon thatis known to occur near certain heteroclinic cycles that con-nect an equilibrium and a periodic orbit (EtoP cycle). Itcan be shown numerically that there are other connectingorbits in its neighbourhood: N-heteroclinic EtoP connec-tions, which take additional excursions along the originalEtoP cycle. We present a method to find and continuethem in parameters.
Thorsten RiessUniversitaet [email protected]
CP8
On the Numerical Integration of One NonlinearParabolic Equation
The author constructs the finite difference scheme toinitial-boundary problem to the following nonlinear
parabolic equation
∂U
∂t= α
(x, t, U,
∂2U
∂x2
)+ β (x, t)
(∂U
∂x
)2
.
For the mentioned scheme the theorems of existence anduniqueness of solution and theorem of its convergence tothe solution of source problem are proved.
Mikheil TutberidzeIlia State UniversityAssociated [email protected]
CP9
Information Propagation Models and Social Net-works
With the rise of social networking platforms such as Face-book and Twitter, it has become easier than ever for ru-mors to propagate through social networks. Various theo-retical frameworks exist to describe the dynamics of infor-mation propagation for such systems, but results for theseframeworks typically do not agree. This talk will identifythe implicit assumptions of some of these frameworks, in-cluding a non-autonomous model which takes into accountthe decaying relevance of the information, with an empha-sis on Twitter.
Michael BuschUniversity of California, Santa [email protected]
Jeff MoehlisDept. of Mechanical EngineeringUniversity of California – Santa [email protected]
CP9
Why Ignoring Your Darwinian Fitness May beAdaptive: Evolutionary Dynamics of MovementStrategies in the Presence of Realistic Constraints
Ecological modelers generally assume that organisms tendto move to maximize their fitness. However, it remains un-clear what movement mechanisms might actually producehigher fitness. We study a single-species, two-patch habi-tat selection model (two coupled ordinary differential equa-tions) and compute analytically an optimal conditionalmovement strategy. We apply tools of adaptive dynam-ics to show numerically that this strategy is evolutionarilyand convergence stable. We demonstrate that higher fit-ness can be achieved by ignoring fitness-dependent cues.
Theodore E. Galanthay, Samuel FlaxmanUniversity of [email protected],[email protected]
CP9
Modelling the Dynamics of Decision-Making onNetworks
A dynamical model using an ensemble of coupled activeelements with coupling via a network has been studiednumerically. The topology of the network and dynami-cal behavior attributed individual elements can make a bigdifference to the spread of information on the network. Re-
102 DS11 Abstracts
sults will be presented, showing the evolution of interactingindividuals on various networks. The results can be inter-preted in the context of the decision-making behavior of amarket of consumers, for example the diffusion of energytechnologies in a social network.
Nick McCullenSchool of MathematicsUniversity of [email protected]
Mikhail IvanchenkoUniversity of Leeds, UKNow at University of Nizhny Novgorod, [email protected]
Vladimir ShalfeevDepartment of Radiophysics,Nizhny Novgorod [email protected]
Alastair M. RucklidgeDepartment of Applied MathematicsUniversity of [email protected]
Tim FoxonSchool of Earth and Environment,University of [email protected]
William GaleSchool of Process, Environmental and MaterialsEngineering,University of [email protected]
CP10
Existence and Stability of Symmetric Periodic SbcOrbits in the Planar Pairwise Symmetric Four-Body Problem
We prove the analytic existence of a symmetric periodicsimultaneous binary collision (SBC) orbit in a regularizedplanar pairwise symmetric equal mass four-body problem.We numerically continue this orbit to unequal masses 1,m, 1, m with 0 < m < 1, and numerically investigate thestability of these orbits. This shows that stability seems tooccur when 0.538 ≤ m ≤ 1 and instability seems to occurwhen 0 < m < 0.537.
Lennard F. BakkerBrigham Young [email protected]
Tiancheng OuyangBrigham Young UniversityProvo, UT [email protected]
Duokui YanChern Institute of MathematicsNankai University, [email protected]
Skyler SimmonsBrigham Young [email protected]
CP10
Improving Hurricane Forecasts Using UnmannedAircraft: Motion Coordination in a Strong Flow-field
This talk describes progress on collaborative research thatcombines mathematical tools from aerospace engineering,data assimilation, and atmospheric science in an effort toimprove the accuracy of hurricane forecasts using a fleetof unmanned aircraft. Hurricane-force winds are a majorobstacle to multi-aircraft path planning. Existing resultsfor motion coordination often fail to converge in winds thatexceed the vehicle speed. This talk introduces preliminaryresults on feasible trajectories and motion coordination instrong winds.
Levi DeVries, Angela MakiUniversity of MarylandDepartment of Aerospace [email protected], [email protected]
Doug Koch, Sharan MajumdarUniversity of MiamiRosenstiel School of Marine and Atmospheric [email protected], [email protected]
Derek A. PaleyUniversity of MarylandDepartment of Aerospace [email protected]
CP10
From Systematic Search to Systematic Proof
IIn dynamical systems, periodic orbits represent a groupof important objects to describe the nature of the system.Some authors have developed powerful algorithms to per-form a systematic search of p.o. However, those are onlynumerical approximations. Here we present a ComputerAssisted Proof method to produce rigorous results, usinginterval arithmetic for operations. As result we presentrigorous “skeletons’ of p.o. for different systems.
Marcos RodriguezUniversity of ZaragozaUniversidad de [email protected]
Roberto BarrioUniversity of Zaragoza, [email protected]
CP12
Analyzing the Bifurcations of Ergodic Tori Using aSecond Poincare Section
We consider the local bifurcations that can happen to aquasiperiodic orbit in a 3-dimensional map: (a) a torusdoubling resulting in two disjoint loops, (b) a torus dou-bling resulting in a single closed curve with two loops, (c)the appearance of a third frequency, and (d) the birth ofa stable torus and an unstable torus. We analyze thesebifurcations in terms of the stability of the point at whichthe closed invariant curve intersects a “second Poincaresection’. We show that these bifurcations can be classifieddepending on where the eigenvalues of this fixed point crossthe unit circle.
Soumitro Banerjee
DS11 Abstracts 103
Indian Institute of Science education & Research,Kolkata, [email protected]
Damian GiaourisSchool of Electrical, Electronic and ComputerEngineeringNewcastle University, [email protected]
CP12
Modelling and Dynamics of Lasers Coupled by aPassive Resonator
The modelling of spatially extended coupled lasers requiresan accurate description of the nonlinear interaction of theindividual lasers. Here, we decompose the spatiotempo-ral optical fields into spatial eigenmodes of the entire cou-pled system. The resulting composite cavity model is S1-symmetric and we describe different methods to reducethis symmetry, without introducing algebraic singularities.This greatly facilitates the use of numerical continuationto study the locking/unlocking transitions of the coupledlaser system.
Hartmut Erzgraber, Sebastian M. WieczorekUniversity of ExeterMathematics Research [email protected], [email protected]
CP12
Multiple Time Scale Dynamics in the Gyorgyi andField Models of the Belousov-Zhabotinsky Reac-tion
The Gyorgyi and Field model DIII of the BZ reactionreproduces empirically observed behavior at experimentalparameters. Using the methods from multiple time scaledynamics, we show that a delayed/dynamic Hopf bifurca-tion is responsible for generating the behavior in the modelsthat is observed experimentally. We show that the globalreturn mechanism of the model is associated with trajec-tories following a family of stable limit cycles of the layerequation.
Christopher J. ScheperCenter for Applied MathematicsCornell [email protected]
John GuckenheimerCornell [email protected]
CP13
Dynamics of the Data Assimilation Linked Ecosys-tem Carbon Model (dalec)
The Data Assimilation Linked Ecosystem Carbon model(DALEC) is a relatively simple but effective process basedvegetation model, aiming to recreate the carbon cycle offorests. A mathematical analysis of DALEC provides anunderstanding of the dynamics of the model. We are ableto pinpoint value ranges of certain parameters in the model,pertinent to survival of the forest. We also examined theeffect of increasing CO2 in the atmosphere and rising tem-
peratures.
Anna M. ChuterUniversity of Surrey, Guildford, United [email protected]
CP13
The Dynamic Radiation Environment AssimilationModel Project (dream)
DREAM uses Kalman filter like techniques to assimi-late space environment measurements with a physics-basedmodel of the radiation belts. Although more general now,DREAM was designed for measurements from instrumentson GPS and geosynchronous satellites. Like efforts in oceanand atmospheric science, DREAM uses sparse measure-ments to estimate the state of a system governed by par-tial differential equations. From our state estimates, wecan calculate the energetic electron environment for otherorbits.
Humberto C. GodinezLos Alamos National LaboratoryApplied Mathematics and Plasma [email protected]
Andrew M. FraserLos Alamos National [email protected]
CP13
Quantifying Uncertainty in Climate Change Sci-ence Through Empirical Information Theory
Quantifying the uncertainty for the present climate andthe predictions of climate change in the suite of imperfectAtmosphere Ocean Science computer models is a centralissue in climate change science. We develop a systematicapproach to quantify model errors in the climate modelsthrough empirical information theory. Examples with di-rect relevance to climate change science including the pro-totype behavior of greenhouse tracer gases are considered.
Boris GershgorinCourant [email protected]
Andrew MajdaCourant Institute [email protected]
CP14
Optimal Phase Response Curve for Synchroniza-tion of Limit-Cycle Oscillators.
Synchronization phenomena of non-interacting limit-cycleoscillators induced by common noisy signals are analyzed.Poisson impulses and Gaussian white noise are two impor-tant cases of the input signals that facilitate such noise-induced synchronization. We obtain the optimal phaseresponse curve of the oscillator for each case, which mini-mizes the Lyapunov exponent of small phase perturbations.We introduce a class of noisy signal that can be interpo-lated between the Gaussian and Poisson cases and examinethe transition.
Shigefumi Hata
104 DS11 Abstracts
Nonliner Dynamics Group, Department of Physics,Graduate School of Sciences, Kyoto [email protected]
Hiroya NakaoDepartment of PhysicsKyoto [email protected]
CP14
Scalable Parallel Physical Random Number Gen-erator Based on a Superluminescent LED
We describe an optoelectronic system for simultaneouslygenerating parallel, independent streams of random bits us-ing spectrally separated noise signals obtained from a sin-gle optical source. Using a pair of non-overlapping spectralfilters and a fiber-coupled superluminescent light-emittingdiode (SLED), we produced two independent 10 Gb/s ran-dom bit streams, for a cumulative generation rate of 20Gb/s. The system relies principally on chip-based opto-electronic components that could be integrated in a com-pact, economical package.
Xiaowen LiInstitute for Research in Electronics And Applied PhysicsUniversity of [email protected], [email protected]
Adam B. CohenInstitute for Research in Electronics And Applied Physics,Department of [email protected]
Thomas E. MurphyUniversity of Maryland, College ParkDept. of Electrical and Computer [email protected]
Rajarshi RoyUniversity of [email protected]
CP14
Dynamics and Bifurcations of Stochastic Mean-Field Equations
The brain is composed of an extremely large number ofneurons with nonlinear dynamics and interactions, andsubject to noise. Following the works of McKean, Sznit-man, and Tanaka, we rigorously derive a novel Mean-Fieldequation for the dynamics of infinitely many interactingneurons. In contrast with standard approaches, it is aninfinite-dimensional implicit equation on the probabilitydistribution of the solution. We analyze the existence,uniqueness, stability and bifurcations of the solutions ofthese new equations for standard neuronal models andcompare the obtained dynamics to more customary ap-proaches.
Jonathan D. TouboulDepartment of Mathematical PhysicsThe Rockafeller [email protected]
CP15
On the Origin and Nature of Finite-Amplitude In-
stabilities in Physical Systems
Finite-amplitude instabilities are ubiquitous, but their the-ory and precise definitions require clarification. In thiswork, we discuss the interrelation of various notions con-nected with finite-amplitude instabilities and offer a precisecontext for these phenomena. Then we establish a connec-tion between nonnormality of linear operators, energy con-servation by nonlinear operators and the existence of finite-amplitude instabilities in finite- and infinite-dimensionaldynamical systems, both in the conservative and dissipa-tive cases. This is a joint work with Prof. Jerrold Marsden.
Rouslan KrechetnikovDepartment of Mechanical EngineeringUniversity of California at Santa [email protected]
CP15
Low-Dimensional Models and Anomaly Detectionfor TCP-like Networks Using the Koopman Oper-ator
Given a family of observables on a TCP-like network, alow-dimensional model is extracted from data by projectingonto the associated eigenmodes of the Koopman operator.It is not guaranteed that these eigenmodes are orthogo-nal which requires an oblique projection onto this basis,in contrast to a POD-Galerkin approach. The evolutionof the model is compared with data and used for anomalydetection.
Ryan Mohr, Igor MezicUniversity of California, Santa [email protected], [email protected]
CP15
Analytical Time and Frequency Cause-and-EffectAnalyses Using Volterra Series
In this lecture, generalized analytical first and secondVolterra kernels in time and frequency domains are pre-sented for a nonlinear second order system as a paradigmfor many dynamic systems. Step and periodic inputs arealso employed to quantify and qualify the nonlinear re-sponse characteristics from the system’s fundamental com-ponents. The proposed analytical solution shows the abil-ity of Volterra-based model to predict and understandthe nonlinear system behavior beyond that attainable bylinear-based models.
Ashraf Omran, Brett NewmanOld Dominion UniversityMechanical and Aerospace [email protected], [email protected]
CP17
An Arbitrary Stokes Flow in and Around a LiquidSphere
Stokes flows past liquid spherical boundaries are discussed.In particular, a method of solution to discuss the problemof an arbitrary unsteady Stokes flow past a liquid sphereis presented by employing a recent solution of unsteadyStokes equations. The surface equation of the deformedsphere is determined up to the first order approximation.This method can be extended to study singularity driven
DS11 Abstracts 105
flows inside a liquid sphere.
Sripadmavati BhavarajuDepartment of Mathematics & Statistics,University of Hyderabad, Hyderabad - 500046, [email protected]
CP17
Stirring and Mixing in a Stokes’ Flow: TopologicalChaos, Almost Invariant Sets, and Lobe Dynamics
Stretching rate is a well-known measure of chaos that ischaracteristic of a well-stirred fluid system. However, highstretching rate is not always accompanied by optimal mix-ing. We consider time-dependent Stokes’ flow in a lid-driven cavity as an example system for studying the re-lationship between stretching and the homogenization of apassive scalar concentration. We explain this relationshipusing the topology of almost invariant set motions and lobedynamics.
Mohsen Gheisarieha, Mark StremlerVirginia [email protected], [email protected]
CP17
Low Dimensional Models for Optimal Streaks inthe Blasius Boundary Layer
This talk is concerned with the low dimensional structureof optimal streaks in the Blasius boundary layer. Op-timal streaks are well known to exhibit an approximateself-similarity, which consists of the streamwise velocity re-mains almost independent of both the spanwise wavenum-ber and the streamwise coordinate. However, the reasonof this self-similar behaviour is still unexplained, and thisis necessary to identify the low dimensional nature of op-timal streaks. After revisiting the structure of the streaksnear the leading edge singularity, two additional approxi-mately self-similar relations are identified, which allows theapproximate self-similarity description to be completed.Based on these, two low dimensional models are derivedwith one and two degrees of freedom, respectively. Thesimpler model provides a description of optimal streaksthat is independent of the streamwise stage where opti-mal streaks are defined, while the two-equations model in-cludes the effect of streamwise position. Both models areconsistent and provide good approximations.
Maria HigueraE. T. S. I. AeronauticosUniv. Politecnica de [email protected]
Jose VegaE. T. S. I. AeronauticosUniversidad Politecnica de [email protected]
CP18
Effect of Delay in a Lotka-Volterra Type Predator-Prey Model with a Transmissible Disease in thePredator Species
We consider a system of delay differential equations model-ing the predator-prey eco-epidemic dynamics with a trans-missible disease in the predator population. The time lagin the delay terms represent the predator gestation period.
Threshold values for a few parameters determining the fea-sibility and stability conditions of some equilibria are dis-covered and similarly a threshold is identified for the dis-ease to die out. Hopf bifurcations are investigated in thepresence of zero and non-zero time lag.
Sabiar RahamanDepartment of Mathematics, SSHS, [email protected]
Sabuddin SarwardiDepartment of Mathematics, Aliah University, [email protected]
Mainul HaqueUniversity of Nottingham, UK (Malaysia Campus)[email protected]
CP18
Complexity in a Prey-Predator Delayed Modelwith Modified Leslie-Gower and Holling-Type IISchemes
The complex dynamics is explored in a delayed prey preda-tor model with modified Leslie-Gower scheme and Hollingtype-II functional response. The existence of periodic solu-tions via Hopf-bifurcation with respect to delay parametersare established. The complex dynamical behavior of thesystem outside the domain of stability is evident from theexhaustive numerical simulation. The Properties of Hopfbifurcation are also determined using normal form theoryand center manifold argument.
Anuraj Singh, Sunita GakkharDepartment of MathematicsIIT [email protected], [email protected]
CP19
Hebbian Learning in Hopfield Networks Leadsto Reaction-Diffusion Equations on GeometricalShapes.
We show that a Hopfield network, coupled to a learningequation (Hebbian with decay), stimulated by a periodicinput can be averaged and derived from an energy, whichimplies convergence of the network connectivity. Then, weinterpret the dynamics with fixed weights as an equivalentreaction-diffusion equation on a high dimensional geomet-rical support prescribed by the inputs. Restricting this ge-ometrical support dimension leads to classical patchy cor-tical maps observed in the visual cortex, for instance.
Mathieu N. GaltierINRIA Sophia, NeuroMathComp [email protected]
Olivier FaugerasINRIA [email protected]
Paul C. BressloffUniversity of Utah and University of Oxford, UKDepartment of [email protected]
CP19
Illusory Persistent States in a Model of Visual Mo-
106 DS11 Abstracts
tion Perception
We explore the solution structure in a model of motion es-timation in which the cortical activity is described by cou-pled integro-differential equations. A fixed-velocity visualstimulus produces coexisting stable solutions, or persistentstates, that represent different percepts. Bifurcations ofthese solutions are related to changes in the way that thevisual stimulus can be interpreted. Numerical and analyt-ical tools are applied in order to classify the bifurcationstructure in terms of key parameters.
James Rankin, Olivier Faugeras, milien Tlapale, RomainVeltz, Pierre KornprobstINRIA [email protected], [email protected],[email protected], [email protected],[email protected]
CP19
Patterns of Excitation Waves in Cerebral Cortex
We describe propagating wave patterns in rodent cortexobserved by voltage-sensitive dye imaging. Plane/targetwaves and rotating spiral waves occur frequently duringdelta dominant state (slow wave sleep) and theta domi-nated state (rodent REM sleep). Cortex in vivo is forcedto oscillate with multiple rhythms generated in thalamusand other structures. Spirals as an emergent organizer ofspatiotemporal patterns, can interact with thalamocorti-cally generated rhythms in the cortex, resulting in simpli-fied patterns organized by the rotating wave.
Jian-Young WuGeorgetown UniversityPhysiology and [email protected]
CP20
Phase Oscillator Networks with Star-Like Cou-pling: Bifurcation Analysis
Although our interest to this subject is inspired by atten-tion modeling, phase oscillator networks may be helpful inneurobiology, physics, etc. A network with a central oscilla-tor (CO) and N peripheral oscillators (POs) is studied. De-tailed bifurcation analysis (N=2 and N=3) identifies para-metric regions corresponding to different dynamical modes.Conditions for multistable regime of in-phase and anti-phase synchronization between the CO and groups of POsare described. Other possible regimes include quasiperiod-icity, chimera-like states and chaos.
Oleksandr BurylkoInstitute of MathematicsUkranian academy of [email protected]
Yakov KazanovichInstitute of Mathematical Problems in BiologyRussian Academy of [email protected]
Roman M. BorisyukSchool of Computing and MathematicsUniversity of Plymouth, [email protected]
CP20
Dynamical Properties of the Repressilator Model
We study dynamical properties of an artificial regulatoryoscillator called repressilator. Oscillations arise from theexistence of an absorbing torus-like region in the phasespace of the model. This geometric structure requiresmonotonic repression at all promoters and the absence ofany regulatory connections apart from a cyclic repressionloop. If the cyclic repression is strong, a pair of diffusivelycoupled repressilators displays fast synchronization similarto that in relaxation oscillators.
Alexey KuznetsovIndiana University-Purdue University [email protected]
CP20
Sensitivity Analysis of Phase Response Curves
The Phase Response Curve (PRC) has proven a usefultool for the reduction of complex oscillator models to one-dimensional phase models. We introduce the sensitivityanalysis of this important mathematical object and its nu-merical implementation. As an application, we study sim-ple biochemical models of circadian oscillators and discusshow sensitivity analysis helps drawing connections betweenthe state-space model of the oscillator and its phase re-sponse curve.
Pierre SacreUniversite de [email protected]
Rodolphe SepulchreUniversity of [email protected]
CP21
Structural Properties and Models for MultilevelNetworks
Many real-life complex systems, such as social or commu-nication networks, can be modeled by using networks witha mesoscaled structure, but until very recently there wereno sharp mathematical models to analyze these phenom-ena. In this talk we will present the metric and structuralproperties of multilevel networks which are one of the lat-est models that fit meso-scaled structures and we also givesome randomized growing models to produce such objects.
Miguel RomanceDepartamento de Matematica AplicadaUniversidad Rey Juan [email protected]
Regino Criado, Julio Flores, Alejandro Garcia del AmoUniversidad Rey Juan [email protected], [email protected],[email protected]
Jesus Gomez-GardenesUniversidad de [email protected]
DS11 Abstracts 107
CP21
Unveiling Multi-functional Proteins by Means ofthe Synchronization Properties of the PPI Network
By considering the network of the physical interactions be-tween proteins of the yeast together with a manual and sin-gle functional classification scheme, we introduce a methodable to reveal important information on protein function,at both micro- and macro-scale. In particular, the inspec-tion of the properties of oscillatory dynamics on top of theprotein interaction network leads to the identification ofmisclassification problems in protein function assignments,as well as to unveil correct identification of protein func-tions. We also demonstrate that our approach can givea network representation of the meta-organization of bi-ological processes by unraveling the interactions betweendifferent functional classes.
Irene Sendina-NadalUniversity of Rey Juan Carlos, Madrid, [email protected]
Yanay OfranBar Ilan [email protected]
Juan A. AlmendralUniversity of Rey Juan CarlosMadrid, [email protected]
Javier BulduUniversidad Rey Juan [email protected]
Inmaculada LeyvaUniversity of Rey Juan CarlosMadrid, [email protected]
Daqing LiDepartment of physicsBar Ilan [email protected]
Shlomo HavlinBar-Ilan [email protected]
Stefano BoccalettiCNR-Istituto dei Sistemi [email protected]
CP21
Complex Networks Mesoscopically Characterizedby IPO: Courtship Grammar Beyond Chance
Complex noiseless dynamical systems can be representedin a compressed manner by unstable periodic orbits. Thismethod is extended to describe the similarity of noisy sys-
tems. As an application, we consider Drosophila′s pre-
copulatory courtship, for which we reveal the existence of acomplex grammar. More specifically, we extract the gram-mar (or: the automaton) class it belongs to, which pointsat a power similar to that of human communication.
Ruedi Stoop
Institute of Neuroinformatics ETHZ/UNIZH
CP22
The Iterated Traveler’s Dilemma: Seeking Stabilityin An Unstable Action Space
The ITD is a two-person, non-zero-sum game that con-trasts (i) a unique Nash equilibrium that corresponds tovery low payoffs, with (ii) a unique yet highly unstableaction pair that maximizes social welfare. By pitting sev-eral strategies against one another in a round-robin styletournament, we hope to gain some understanding of theasymptotic behavior of strategy pairs and how competi-tors can settle into highly lucrative yet unstable points,despite what classical game theory suggests.
Philip DaslerDepartment of Computer ScienceUniversity of [email protected]
Predrag TosicUniversity of [email protected]
CP22
Prediction of Computer Dynamics
Building on recent work that establishes that computer sys-tems can be effectively analyzed using a dynamical systemsapproach, we use time-series methods to forecast processorand memory usage patterns. Even a short-term predic-tion of these quantities can be effective in tailoring systemresources ’on the fly’ to the dynamics of a computing ap-plication.
Joshua T. GarlandUniversity of Colorado at BoulderDepartment of Applied [email protected]
Elizabeth BradleyUniversity of ColoradoDepartment of Computer [email protected]
CP22
Statistics of Branched Flow Structure in OpticalMedia
Freak waves arise in areas of significant interest such asocean dynamics and two-dimensional electron gas systems.We find that these exotic waves can occur in optical me-dia with random disorders in the refractive index, and theassociated high-intensity distribution follows a power-law.We develop an analytic theory to explain the power-lawbehavior. The occurrence of freak waves may have impli-cations to metamaterial-based device operations.
Xuan Ni, Wenxu WangElectrical EngineeringArizona State [email protected], [email protected]
Ying-Cheng LaiArizona State UniversityDepartment of Electrical Engineering
108 DS11 Abstracts
CP23
A Dynamical Model of the Innate Immune Re-sponse in the Lungs
The immune system of the lungs has many unique fea-tures not captured by mathematical models of the generalimmune system. We propose a set of differential equationsthat accurately model many of these known features of pul-monary innate immunity and analyze these equations. Weshow that their solutions have basic dynamical propertieswhich agree with experimental results in the pulmonaryimmune system.
Richard BuckalewUniversity of [email protected]
Todd YoungOhio UniversityDepartment of [email protected]
Erik M. BoczkoDepartment of Biomedical InformaticsVanderbilt University Medical [email protected]
CP23
Development of a Model of Human CardiovascularSystem and Heart Rate Variability
We have developed a model of cardiovascular system thatincludes baroreflex (a sophisticated multi-feedback nonlin-ear dynamical system), the pulsating heart, and mechani-cal effect of respiration. The model is parameterized bymatching the time dependence and frequency spectrumof heart period produced by the model with experimentaldata under regular and paced breathing conditions. Theparameterization and analysis of the model have been per-formed by using our software GoSUM (Global Optimiza-tion, Sensitivity and Uncertainty in Models).
Vladimir FonoberovChief ScientistAIMdyn, [email protected]
Igor MezicUniversity of California, Santa [email protected]
Marsha BatesRutgers [email protected]
CP23
Gradient Flow Model for Osmotic Cell Swelling
A basic model for cell swelling by osmosis is constructed,resulting in a free boundary problem. For radially sym-metric initial conditions, this model can be formulated asa gradient flow on a metric by choosing a suitable pair offunctional and metric. This particular choice does not re-quire the osmotic force to be included in the formulationexplicitly. It appears that this result can be generalized to
non-symmetric initial conditions.
Martijn ZaalVU University [email protected]
CP25
A Neutral Theory of Speciation Matching Empiri-cal Diversity
The number of living species on Earth has been estimatedto be between 10 and 100 million. Understanding the pro-cesses that have generated such remarkable diversity is oneof the greatest challenges in evolutionary biology. We pro-posed recently a new topopatric mechanism of speciation inwhich a population, with genetically identical individualshomogeneously distributed in space, spontaneously breaksup into species when subjected to mutations and to twomating restrictions: individuals can select a mate only fromwithin a maximum spatial distance S from itself and if thegenetic distance from the selected partner is less than amaximum value G. Species develop depending on the mu-tation rate and on the parameters S and G. The numberof species fluctuate in time, reflecting a dynamical balancebetween extinctions and speciation events. The resultingspecies-area relationships and abundance distributions areconsistent with observations in nature. Finally we considervariations in the topology of the environment, simulatingnearly one-dimension geometries (rivers) and rings.
Marcus A. AguiarUniversidade Estadual de [email protected]
Yaneer Bar-YamNew England Complex Systems InstituteCambridge, MA, [email protected]
Michel BarangerMITCambridge, MA, [email protected]
Les KaufmanBoston UniversityBoston, MA, [email protected]
Elizabeth BaptestiniIFGW - UNICAMPCampinas, SP, Brazil, [email protected]
Ayana MartinsIB - USPSao Paulo, SP, Brazil, [email protected]
CP25
Mesoscale Analysis of Porous Soil Networks
Porous structure of soils using complex network modelsbased on heterogeneous preferential attachment scheme ispresented. Pores are considered as nodes and the linksbetween them are determined by an affinity function thatdepends on their intrinsic properties. To simulate the soiltextures, an application to different real soils is presented.
DS11 Abstracts 109
Analysing these networks at mesoscale level, communitystructure that depends on the pore size distributions andtheir spatial location has been found
Rosa M. Benito, Juan Pablo Cardenas, Antonio Santiago,Ana Tarquis, Juan Carlos LosadaUniversidad Politecnica de [email protected],[email protected], [email protected],[email protected], [email protected]
Florentino BorondoUniversidad Autonoma de [email protected]
CP25
Analysis of the Pattern Formation in Various Mod-els of Hormone Transport
Abstract not available at time of publication.
Delphine DraelantsDept. Mathematics and Computer ScienceUniversiteit Antwerpen, [email protected]
CP26
Fluctuation Analysis Via Synthetic Diffusion
Detrended Fluctuation Analysis (DFA) probes signal fluc-tuations for long range correlations, evidenced by power-law scaling. We show: DFA is intimately related to R/SAnalysis, cannot ”detrend”, exhibits significant bias forshort time windows, and the least-squares fitting used toestimate scaling is inefficient and detrimentally affected bythe biased region. We demonstrate that standard diffu-sion measurement is an unbiased equivalent of the heuris-tic DFA and R/S methods and develop an more efficientweighted least squares scheme.
Robert BryceR&D Canada Centre for Operational Research andAnalysis101 Colonel By Drive, Ottawa ON, K1A 0K2, [email protected]
CP26
Nonlinearities in Stocks As a Consequence of Socio-Political Events: Classification of Events Trigger-ing Nonlinearity in Stock Exchange
We propose that socio-political and economical events canbe classified using Hinich-Portmanteau-Bicorrelation testwith Windowing technique. We use BSE-100 index andKSE-100 index returns data for analysis and it is concludedthat magnitude of an event should be considered a measureof impact on stock markets. The present study also revealsmarket mentality towards a specific event, thus how long aspecific trend lasts is an important viewpoint for investorsand scientists in the field.
Syed Nasir Danial, Rosheena Siddiqi
Bahria University (Karachi Campus)[email protected], [email protected]
CP26
Chaotic Fluctuations in Stocks in a Market : Ap-
proximating with the Duffing-Oscillator Model
Speculations combined with supply demand inelasticitiesmay render the commodity system unstable in the face ofdisturbances. Changes in stocks of agricultural commodi-ties are affected by production responses to price changesand speculations. Such nonlinear interactions incorporat-ing delays in a market may explain the commodity oscil-lations. We approximate the nature of market conditionsand examine the chaos in the time series of yearly fluctu-ations in stocks of two commodities-rice and wheat withthe Duffing-oscillator model. Statistical tests and correla-tion dimension calculation confirm that the time series isnoise free for rice but contaminated for wheat. The timesignals obtained by Fourier-periodogram analysis are ap-proximated with the deterministic and stochastic Duffing-oscillator models and the parameters are estimated usingan analytical approach (based on harmonic analysis) anda statistical parameter estimation based approach, respec-tively. In both cases the parameters reflect the market con-ditions operating for the commodities during the period.We obtain phase portraits and lyapunov exponents of themodel for the estimated parameters which show that thebehavior is non-chaotic for different driving frequencies incase of rice whereas it may be chaotic for wheat. Howeverthe stochastic model reveals the noise in the estimation andconfirms that the estimation is much more reliable for ricethan wheat. While several methods verify noise-inducedtransitions to chaos, present work attempts to show thatnoise renders the estimation unreliable. Exogenous ran-dom shocks or simply measurement errors may distort thesystem dynamics/stability making it appear chaotic. Sincechaos is generated endogenously, our results may indicatethat interactions between market forces lead to regular be-havior in commodity stocks in the absence of random in-fluences. The latter has policy implications and remains amoot issue.
Varsha S. KulkarniIndiana University [email protected]
Raghav GaihaUniversity of [email protected]
CP27
Bifurcation and Stability Properties for Asymptot-ically Asymmetric Slowly Non-Dissipative Equa-tions
In this talk I will present recent work on bifurcation, stabil-ity, and nodal properties for scalar parabolic PDEs of theform ut = uxx +b+u+−b−u−+g(u). I will discuss how thestructure of the 3-dimensional bifurcation diagrams andthe interconnectedness of the nodal and stability proper-ties of the stationary solutions are key to the extension ofglobal attractor theory to reaction-diffusion equations withjumping nonlinearities.
Nitsan Ben-GalDepartment of Computer Science & Applied MathematicsThe Weizmann Institute of [email protected]
Kristen MooreUniversity of [email protected]
Juliette Hell
110 DS11 Abstracts
Freie Universitat BerlinInstitut fur [email protected]
CP27
Existence and Regularity Result for Functional In-tegrodifferential Equations with Finite Delay ViaFractional Operators: An Application to BacterialGrowth And Multilication .
This work is concerned with the strict solution for partialfunctional integrodifferential equations with finite delay ina Banach space. The results are obtained by using theresolvent operators and Banch type fixed point theorem,in the context of fractional operators.
Hechmi HattabENIT-LAMSIN - Tunis [email protected]
CP27
Some Applications of Differential Galois Theory inDynamical Systems
Differential Galois theory is an extension of the classicalone to differential equations and it treats the problem on in-tegrability of differential equations by quadratures. In thistalk, using the differential Galois theory, we discuss bifurca-tions of homoclinic orbits and Sturm-Liouville type eigen-value problems on the infinite interval. Roughly speaking,we give the following results.Theorem 1. The differential Galois groups for variationalequations around homoclinic orbits are triangularizable un-der some nondegenerate conditions if their saddle-node orpitchfork bifurcations occurs.Theorem 2. The differential Galois groups for Sturm-Liouville type eigenvalue problems are triangularizable un-der some nondegenerate conditions if they have a solution.It is a well-known fact in the differential Galois theory thatdifferential equations are integrable by quadratures if theirdifferential Galois groups are triangularizable. Finally, weapply the theory to two examples: bifurcations of pulsesin coupled real Ginzburg-Landau equations and spectralstability of a traveling front in the Allen-Cahn equation.Numerical results are also given. This is a joint work withDavid Blazquez-Sanz of Sergio Arboleda University in Bo-gota, Colombia.
Kazuyuki YagasakiNiigata UniversityDepartment of Information [email protected]
CP28
Lagrangian Coherent Structures in AerobiologicalTransport
An emerging application of Lagrangian coherent structures(LCSs) is to aerobiology, specifically the study of biologi-cal transport through the atmosphere, where one predictsthe motion of fluid-borne microbes whose population struc-ture may be linked with LCSs. We report recent interdis-ciplinary work in this area, which involves a collaborationof biologists and dynamicists. We also address the issue ofaccurate prediction of LCSs based on meteorological fore-casts, which guides our atmospheric sampling efforts.
Amir E. BozorgmaghamVirginian tech
Shane D. RossVirginia TechEngineering Science and [email protected]
David SchmaleVirginia [email protected]
Phanindra TallapragadaUniversity of North [email protected]
CP28
Fast Computations of Lagrangian Coherent Struc-tures in 2 and 3 Dimensions
Lagrangian coherent structures (LCS) offer an appealingtool for analysis of transport and mixing in fluid flows withgeneral time dependence. Much recent work has focusedon efficient computations of LCS to reduce the necessarycomputational time. We present recent work focusing onridge- and surface-tracking algorithms for fast computa-tions of LCS with applications to several biological andgeophysical flows.
Douglas M. LipinskiUniversity of Colorado at [email protected]
Kamran MohseniUniversity of Florida, Gainesville, [email protected]
CP28
Invariant Manifolds in ChaoticAdvection-Reaction-Diffusion Systems
Invariant manifolds are well known organizing structuresin chaotic advection. We consider reaction-diffusion dy-namics within a fluid simultaneously undergoing chaoticadvection. Prior work demonstrates that such systems gen-erate ”burning fronts” with rich structure, including modelocking. We construct invariant manifolds that incorporatethe additional reaction-diffusion dynamics. They providea clear criterion for mode locking and an explanation ofthe front patterns. We also present results on direct exper-imental measurements of such manifolds.
John R. MahoneyUniversity of California, [email protected]
Kevin A. MitchellUniv of California, MercedSchool of Natural [email protected]
Tom SolomonDept. of Physics and AstronomyBucknell University, Lewisburg, PA, [email protected]
CP29
Multistability Analysis Via a Lyapunov-Based Ap-
DS11 Abstracts 111
proach
This talk focuses on multistability theory for discontinuousdynamical systems having multiple isolated and a contin-uum of equilibria. Multistability is the property wherebythe solutions of a dynamical system alternate between twoor more mutually exclusive Lyapunov stable and conver-gent equilibrium states over time. In this talk, we extendthe definition and theory of multistability to discontinuousautonomous dynamical systems. In particular, nontan-gency Lyapunov-based tests for multistability for discon-tinuous systems with Filippov and Caratheodory solutionsare established. The results are then applied to excitatory-inhibitory biological neuronal networks to explain the un-derlying mechanism of action for anesthesia and conscious-ness from a multistable dynamical system perspective.
Qing HuiDepartment of Mechanical EngineeringTexas Tech [email protected]
CP29
Discontinuity Geometry - An Alternative Way toAnalyse Impacting Systems
Periodically-forced impact oscillators may undergo bothstandard (smooth) bifurcations and grazing bifurcationsand it is well-known that under parameter variation there issometimes a saddle-node bifurcation present in the neigh-bourhood of a grazing bifurcation and sometimes it is ab-sent. Here we will use discontinuity-geometry to analysethe saddle-node and grazing bifurcation relationship andexplain why a saddle-node bifurcation can sometimes befound in the vicinity of a grazing bifurcation and why itsometimes is absent.
Neil Humphries, Petri PiiroinenSchool of Mathematics, Statistics and AppliedMathematicsNational University of Ireland, [email protected], [email protected]
CP29
Non-Smooth Bifurcations in a Sustainable Devel-opment Model
Sustainable development in a community plays an im-portant role in environmental and social sciences. Mod-elling such systems includes coupling of population, ecosys-temic, economic and social variables. In our 4-dimensionalmodel we found Hopf, saddle-node bifurcations and chaoticmotion. When two such communities are linked in acommerce-exchange scenario, where commerce conditionsdepend on the state variables, the whole system becomesnon-smooth. We found non-smooth bifurcations when thecommerce conditions, which depend on parameters, arevaried.
Gerard OlivarDepartment of Electrical and Electronics EngineeringUniversidad Nacional de Colombia, sede [email protected]
Jorge AmadorCeiBA ComplexityUniversidad Nacional de Colombia, sede [email protected]
David AnguloDepartment of Electrical and Electronics EngineeringUniversidad Nacional de Colombia, sede [email protected]
Hector GranadaUniversidad Nacional de Colombia, sede [email protected]
CP30
A Systems-Biology Investigation of Heat-ShockProtein Regulated Gene Networks: MathematicalModels, Predictions and Laboratory Experiments
A mathematical model is proposed of the Heat-shock pro-teins (which is initiated in all living organisms wheneverproteins are damaged by metal stress) regulatory network.We perform a detailed mathematical analysis (includingstability, bifurcation and asymptotic studies) and inves-tigate the influence of single and mixed stress (divalentplus trivalent) responses; particularly mixtures of two sim-ilar divalent metal ions produce additive effects, whereasmixtures of two dissimilar metals show interfering effects.Laboratory experiments confirm these predictions.
Mainul Haque
University of Nottingham, UK (Malaysia Campus)[email protected]
John KingUniversity of [email protected]
David dePomaraiSchool of BiologyUniversity of Nottingham, [email protected]
CP30
Analysis and Design of a Versatile Synthetic Net-work for Inducible Gene Expression in MammalianSystems
We present a mathematical model for a novel syntheticgene regulatory network. The aim of this circuit is to act asa bistable switch for in vivo delivery of short hairpin RNA(shRNA) which can induce RNA interference (RNAi) of atarget mRNA. We will show how the circuit can be con-trolled to induce sustained expression of a shRNA, usingthe transient input of two different inducer molecules.
John HoganBristol Centre for Applied Nonlinear MathematicsDepartment of Engineering Mathematics, University [email protected]
CP30
The Nonlinear Dynamics of Transcription Regula-tion in Mammalian Timekeeping
Mammalian time-keeping plays a crucial role in coordinat-ing many physiological functions (including but not limitedto) sleep, cell cycle, metabolism, and calcium regulation.This master clock is hypothesized to be governed by theSupra-Chiasmatic Nuclei (SCN). Each cell in the SCN is anautonomous oscillator driven by a negative feedback loopinvolving core clock proteins; inter-cellular coupling mecha-
112 DS11 Abstracts
nisms enables synchronization within this network of cells.Without this synchronization, the SCN cannot properlyfunction. In this talk, we discuss two recent results of non-linear regulation mechanisms in mammalian time-keeping.We start by exploring a simple model of transcription thatresults in chaotic behavior in a single cellular oscillator.We then focus attention on a detailed model of SCN cells,with each cell coupled to form a SCN network; we find thatvarying the level of the BMAL core clock protein acts as atuning parameter, which determines whether stable oscil-lations in SCN network will occur. Most surprisingly, theseresults have been verified by experiments. This talk is thebased on joint work with Danny Forger.
Richard YamadaUniversity of [email protected]
CP32
Investigating Global Brain States Using EmpiricalMode Decomposition Based Weighting FunctionAnalysis and Permutation Based Entropic Mea-sures
Permutation entropy, a symbolic dynamic measure of fluc-tuations, is combined with EMD and weighting func-tion analysis to investigate nonlinear and non-stationarydynamical systems. This approach has potentiallywidespread applicability in the nonlinear sciences, but em-phasis here is upon digital recordings of EEG and MEG inhuman, task free, resting and sleep states. The analysespresented provides new insights into temporal changes inglobal brain state reflected in the quantitative dynamics ofthe brain’s electromagnetic fields.
John L. AvenSan Diego State UniversityDepartment of Mathematicschaotic [email protected]
Arnold MandellCielo [email protected]
Tom Holroyd, Richard CoppolaNIH-NIMHCore MEG [email protected], [email protected]
CP32
A General Theory of Percolation Thresholds forNetworks
Percolation on networks has applications ranging from epi-demic and information spreading to system robustness.Extending previous results restricted to directed or Marko-vian networks, we introduce a general theory for predictingthe percolation threshold based on an analysis of the net-work adjacency matrix. In addition to its applicability fornetworks with non-Markovian statistics, our method is eas-ily implemented when the adjacency matrix is known. Weillustrate our theory with various examples.
Dane TaylorDept. Applied MathUniversity of [email protected]
Juan G. Restrepo
Department of Applied MathematicsUniversity of Colorado at [email protected]
CP32
Noise Bridges Dynamical Correlation and Topol-ogy in Coupled Oscillator Networks
We study the relationship between dynamical propertiesand interaction patterns in complex oscillator networks inthe presence of noise. A striking finding is that noise leadsto a general, one-to-one correspondence between the dy-namical correlation and the connections among oscillatorsfor a variety of node dynamics and network structures. Theuniversal finding enables an accurate prediction of the fullnetwork topology based solely on measuring the dynamicalcorrelation. The power of the method for network infer-ence is demonstrated by the high success rate in identify-ing links for distinct dynamics on both model and real-lifenetworks. The method can have potential applications invarious fields due to its generality, high accuracy, and effi-ciency.
Wenxu WangElectrical EngineeringArizona State [email protected]
Ying-Cheng LaiArizona State UniversityDepartment of Electrical [email protected]
Jie Ren, Baowen LiDepartment of Physics and Centre for ComputationalScienceand and Engineering, National University of [email protected], [email protected]
CP33
New Computational Methods for Open Dynamics
We will present a new class of constrained optimisationbased methods for approximating dynamically interestingobjects in open systems, including conditionally invari-ant measures, locally invariant sets and exponential escaperates. We have successfully applied similar methods to thecomputation of invariant measures for closed systems (Boseand Murray, SIAM J Opt, 2007), but open systems presentsignificant additional difficulties due to non-convexity ofthe underlying optimisation problems. The talk will intro-duce approach, describe the theoretical challenges and givea couple of examples.
Rua MurrayDepartment of Mathematics and StatisticsUniversity of Canterbury, [email protected]
Christopher BoseDept Mathematics & StatisticsUniversity of [email protected]
CP33
Recent Advances in Mostly Conjugacy
Two dynamical systems are considered to be the the same,
DS11 Abstracts 113
if there exists a conjugacy between them. This is seldomobserved in real world modeling. The past works of Bolltand Skufca, have developed a systematic methodology tocompare systems which are not quite conjugate, coiningthe phrase “mostly conjugacy”. We now extend “mostlyconjugacy” to stochastically perturbed dynamical systems.We also describe a recent direction, where a Monge Kan-tarovich approach is adopted.
Rana D. Parshadclarkson [email protected]
Erik BolltClarkson [email protected]
joe skufcaclarkson [email protected]
Jiongxuan ZhengClarkson [email protected]
CP33
A Conjecture of Lorenz: Transitive Plus Nonin-vertible Implies Sensitive
In a 1989 paper, ”Computational chaos - a prelude to com-putational instability,” E. Lorenz conjectured that a mapwith an attractor on which two distinct points mappedto the same image point must be chaotic. He provided a”nonrigorous argument” which did not turn out to lead to aproof. We have precisely formulated and proved his conjec-ture, imprecisely stated as: a noninvertible map having aninvariant set with a dense orbit must exhibit sensitivity toinitial conditions. Lorenz was studying how ”poorly” Eu-ler’s method approximates solutions to a differential equa-tion as the time step is increased. Numerical simulationssuggested that a certain two-dimensional map exhibiteda noninvertible attractor. Since the conjecture is true,this provides strong evidence of chaos. More generally,this conjecture aids the understanding of a noninvertibleroute to chaos via the breakup of an invariant circle. It isalso related to a noninvertible route to chaos involving thebreakup of an invariant circle. We provide a relatively sim-ple proof of this conjecture. The proof requires the additionof a small step to existing results in the literature datingback to Auslander and Yorke [1980], Silverman [1992] andGlassner and Weiss [1993].
Bruce B. PeckhamDept. of Mathematics and StatisticsUniversity of Minnesota [email protected]
Garrett TaftIndiana University - Purdue University [email protected]
CP34
Feedback Control of Traveling and Standing Wavesin the O(2) Equivariant Hopf Bifurcation Problem
The Hopf bifurcation with O(2) symmetry arises naturallyin pattern-formation problems posed on one-dimensionalspatially periodic domains, and leads to both standing and
traveling wave solution branches. We exploit the sym-metries of these solutions to design non-invasive feedbackcontrols that can select and stabilize the targeted solutionbranch, in the event that it bifurcates unstably. If the tar-geted branch bifurcates subcritically, the feedback involvesa time-delay of Pyragas type.
Genevieve BrownNorthwestern [email protected]
Claire M. PostlethwaiteUniversity of [email protected]
Mary C. SilberNorthwestern UniversityDept. of Engineering Sciences and Applied [email protected]
CP34
Stabilizing Trav-eling Waves in the One-Dimensional CGLE UsingSpatio-Temporal Feedback Control
We investigate spatio-temporal feedback control of travel-ing plane wave solutions of the complex Ginzburg-Landauequation in the Benjamin-Feir unstable regime. The feed-back, similar to Pyragas control, exploits the symmetry oftraveling waves in a natural way. An appropriately chosentime-delayed feedback term, compensated with a spatialshift, stabilizes most of the family of traveling waves. Inother instances, a second feedback term that involves onlyspatial shifts is required. Stability results are confirmedusing DDE-BIFTOOL.
Tiffany M. PsemenekiNorthwestern [email protected]
Mary C. SilberNorthwestern UniversityDept. of Engineering Sciences and Applied [email protected]
CP34
Partial Control of Chaotic Transients and EscapeTimes
When we attempt to control a linear system in which somenoise has been added, typically we need a control higheror equal to the amount of noise added. When we havea region in phase space where there is a chaotic saddle,all initial conditions will escape from it after a transientwith the exception of a set of points of zero Lebesgue mea-sure. The action of an external noise makes all trajectoriesescape even faster. Attempting to avoid those escapes byapplying a control smaller than noise seems to be an impos-sible task. Here we show, however, that this goal is indeedpossible, based on a geometrical property found typicallyin this situation: the existence of a horseshoe. The horse-shoe implies that there exists what we call safe sets, whichassures that there is a general strategy that allows one tokeep trajectories inside that region with a control smallerthan noise. We call this type of control partial control ofchaos [Samuel Zambrano, Miguel A. F. Sanjun, and JamesA. Yorke. Partial Control of Chaotic Systems. Phys. Rev.E 77, 055201(R) (2008), Samuel Zambrano and Miguel A.F. Sanjun. Exploring Partial Control of Chaotic Systems.
114 DS11 Abstracts
Phys. Rev. E 79, 026217 (2009)] that allows one to keepthe trajectories of a dynamical system close to the sad-dle even in presence of a noise stronger than the appliedcontrol. In this talk recent progress and new results onthis control strategy related to escapes times [Juan Sabuco,Samuel Zambrano, and Miguel A. F. Sanjun. Partial con-trol of chaotic transients and escape times. New Journalof Physics 12, 113038 (2010)] are presented. This is jointwork with James A Yorke (USA), Samuel Zambrano andJuan Sabuco (Spain).
Miguel SanjuanDepartment of PhysicsUniversidad Rey Juan Carlos, Madrid (Spain)[email protected]
CP35
Pinning of Rotating Waves in Systems with Imper-fect So(2) Symmetry
Experiments in small aspect-ratio Taylor-Couette flowshave reported the presence of a band in parameter spacewhere rotating waves become steady non-axisymmetric so-lutions (pinning) via infinite-period bifurcations that previ-ous numerical simulations were unable to reproduce. Herewe present numerical simulations that include a small tiltof one of the endwalls, simulating the effects of imperfec-tions that break the SO(2) axisymmetry of the problem,and indeed are able to reproduce the experimentally ob-served pinning of the rotating waves. A detailed analysisof the corresponding normal form shows that the problemis more complex than expected.
Francisco MarquesUniversitat Politecnica de CatalunyaDepartment of Applied [email protected]
Alvaro MeseguerDepartment of Applied PhysicsUniversitat Politecnica de [email protected]
Juan M. LopezArizona State [email protected]
RAFAEL [email protected]
CP35
Interaction of Faraday Waves and Cross-Waves
We examine the connection between Faraday waves, whicharise in vertically vibrated systems, and ”cross-waves”,which are found in horizontally forced systems, by combin-ing vertical and horizontal forcing. Ongoing experimentsutilizing two perpendicularly oriented shakers will be de-scribed, including the effect on pattern formation of vary-ing the two forcing frequencies, amplitudes, and phases.These results will be compared with theoretical predictionsbased on an appropriate set of model equations.
Jeff Porter, Ignacio Tinao, Ana Laveron-SimavillaUniversidad Politecnica de [email protected], [email protected],[email protected]
CP35
Nonlinear Three-Wave Interactions and Spatio-Temporal Chaos
Three-wave interactions play a key role in pattern for-mation problems where there are quadratic nonlinearities,such as the Faraday wave experiment. We consider three-wave interactions between two circles of wavevectors, wheretwo modes on either circle can drive one on the other, andshow how mutual reinforcement can lead to complex pat-terns such as quasipatterns and spatio-temporal chaos. Weexplore the dynamics in a model PDE and in the weaklynonlinear Navier-Stokes equations.
Alastair M. RucklidgeDepartment of Applied MathematicsUniversity of [email protected]
Anne SkeldonUniversity of SurreyGuildford, [email protected]
CP36
Manipulating the Excitatory/inhibitory BalanceAlters ¡i¿in Vitro¡/i¿ Dynamical Patterns in Neu-ronal Networks
How are conserved activity patterns altered when thebalance between excitation and inhibition is perturbed?Proper balance is essential for normal brain function, in-cluding cognitive processing and the representation of sen-sory information. When the balance is compromised, neu-rological disorders may result. We use a simple reducednetwork of cultured hippocampal and striatal neurons toinvestigate how manipulating this balance affects synchro-nized bursting activity, the most prominent temporal sig-nature of cultured neural networks.
Rhonda DzakpasuGeorgetown UniversityDepartment of [email protected]
Xin ChenGeorgetown [email protected]
Mark NiedringhausGeorgetown University Medical [email protected]
CP36
Multi-bump Standing Pulses in a Firing RateModel
We study standing pulses in a firing rate model with ageneral class of synaptic couplings and firing rate functions.We present an intrinsic relationship between the underlyingintegral equation and a class of ODEs. Then by trackinginvariant manifolds’ passage near a hyperbolic fixed pointof the ODE, we establish the existence of N-bump homo-clinic orbits that correspond to multi-bump standing pulsesolutions of the integral equation. We also analyze thecoexistence and bifurcations of the multi-bump standingpulse solutions.
Yixin Guo
DS11 Abstracts 115
Drexel UniversityDepartment of [email protected]
Dennis Guang YangDepartment of Mathematics, Cornell [email protected]
CP36
Effect of Nodal Scale on the Analysis of Whole-Brain Anatomical Networks
A number of experimental groups have employed MRI andbiomagnetic imaging to model brain connectivity in livinghumans as anatomical networks. However, different studieshave used very different numbers of nodes when construct-ing their network models, and a wide variation in networkproperties (e.g., small-worldness, path length, and cluster-ing coefficients) has been observed. We present numericalresults discussing whether these variations in network prop-erties with node number are associated with the intrinsicanatomical features of brain networks, or instead emergefrom more general attributes of networks (not specificallyassociated with brain anatomy).
Adam S. LandsbergClaremont McKenna College, Pitzer College, [email protected]
Eric FriedmanORIECornell [email protected]
CP37
Spatial Filter and Backward Time Approach ofProbabilistic Method to Advection Diffusion Equa-tion
Advection diffusion equations can be studied using a prob-abilistic approach to analyze transport of densities. Themotion of diffusive particles is given by the Langevin equa-
tion d �X = �V dt +√
2D d �W . The solution of the advectionequation can be written as an expectation of a functionalwhich is typically evaluated using a monte carlo method.We introduce a new method using backward time integra-tion and spatial averaging. We apply this method to thestudy of the transport of densities by a perturbed cellular,divergence-free velocity field and small diffusion.
Sophie LoireUniversity of California Santa [email protected]
Igor MezicUniversity of California, Santa [email protected]
CP37
Amplitude Equations for the Stochastic Ginzburg-Landau Equation
In this talk, we consider stochastic Ginzburg-Landau orAllen-Cahn equation with degenerate additive noise. Usingthe natural separation of time-scales near a change of sta-bility, we derive rigorously amplitude equations and theirhigher order corrections. We show that degenerate addi-
tive noise has the potential to stabilize the dynamics of thedominant modes.
Wael W. MohammedPhd [email protected]
Dirk BlomkerUniversitat [email protected]
CP37
A Stochastic Boundary Forcing Model for Simulat-ing Wave Turbulence Systems
The beta-Fermi-Pasta-Ulam (FPU) model can serve asan example of a discretized wave turbulence system withfour-wave nonlinear interactions. We present a stochas-tic boundary forcing technique for the numerical simula-tion of a subdomain of a periodic beta-FPU chain, with aview toward modeling the correct time evolution of the en-ergy spectrum more accurately than conventional periodicboundary conditions would.
Warren Towne, Peter R. KramerRensselaer Polytechnic InstituteDepartment of Mathematical [email protected], [email protected]
Yuri V. LvovRensselaer Polytechnic [email protected]
CP38
Transient Chaos in a Damped, Undriven System:The Magnetic Pendulum
Through the example of the magnetic pendulum, we lookat the properties of transient behaviour in dissipative, un-driven systems. First, we look at the fractality of the basinboundaries of the attractors, in this case, the magnetsabove which the pendulum stops. We find that fractal-ity depends on the resolution used for the computation,which means that the properties of the boundary are notscale independent. For example, the plot of the time ittakes the pendulum to stop vs. the initial conditions showsirregular clusters of sudden jumps. To characterise thebehaviour we use finite-scale, time-dependent versions ofthe usual chaos parameters, like Lyapunov exponents, en-tropies, dimensions and escape rates. For the escape rate,in particular, we find that it depends exponentially on time.We compare the results with chaotic scattering in Hamil-tonian systems, where chaos quantities and fractality arewell-defined.
Gyorgy KarolyiBudapest University of Technology and [email protected]
Tamas TelInstitute for Theoretical PhysicsEtovos University, [email protected]
Adilson E. MotterNorthwestern [email protected]
116 DS11 Abstracts
Marton GruizInstitute for Theoretical PhysicsEotvos [email protected]
CP38
Phase Control of Escapes and Basin BoundaryMetamorphoses
Basin boundary metamorphoses are characteristic in somekinds of chaotic dynamical systems. They take place whenone parameter of the system is varied and it passes thor-ough certain critical value. Previous works shown that thisphenomenon involves certain particular unstable orbits inthe basin boundary which are accessible from inside one ofthe basins. In this talk, we show that parametric harmonicperturbations can produce basin boundary metamorphosisin chaotic dynamical systems. The main findings of ourresearch are oriented in both, the study of the fractal di-mension of the basin boundaries and in the study of thevariation of the area of the basin once we change the valueof one suitable parameter [Seoane et al. Europhys. Lett.90, 30002 (2010)]. The physical context of this work isrelated with the phenomenon of particles escaping from apotential well, which is illustrated by using as prototypemodel the Helmholtz oscillator [Seoane et al. Phys. Rev.E 78, 016205 (2008)]. Finally, Melnikov analysis of the re-ported phenomenon has also been carried out. This is jointwork with S. Zambrano, Ines P. Marino, and Miguel A. F.Sanjuan. (Spain).
Jesus M. SeoaneNonlinear Dynamics and Chaos Group.Universidad Rey Juan [email protected]
CP38
Permutation Complexity of Spatiotemporal Dy-namics
In recent years permutation complexity tools has beenshown to be a powerful tool for time series analysis. Thisfamily of tools makes use of any quantity or functionalbased on the order relations (permutations) appearing be-tween consecutive elements of a sequence. In this talk weshow how these tools can also be applied for the analysis ofcomplex spatiotemporal dynamics. The aim of this analy-sis is both to characterize that complexity and to discrim-inate between different types of complex spatiotemporaldynamics. We introduce our ideas making use of CellularAutomata, and we show that our ideas can be used for theanalysis of spatiotemporal data from Coupled Map Lattices(CMLs) and of Magneto Encephalograms (MEGs).
Samuel ZambranoNonlinear Dynamics and Chaos Group.Universidad Rey Juan [email protected]
Jose M. AmigoUniversidad Miguel HernandezCentro de Investigacion [email protected]
Miguel SanjuanUniversidad Rey Juan CarlosDepartamento de Ciencias de la Naturaleza y [email protected]
CP39
Border Collision Bifurcations, Organizing Centers,and Continuity Breaking
We investigate bifurcation structures in piecewise-smoothmaps and demonstrate under which conditions an inter-section of two border collision bifurcation curves in a 2Dparameter plane represents an organizing center where aninfinite number of periodic orbits emerge. Depending onthe local properties of the map on both sides of the bound-ary, we determine the bifurcation structure formed by theseorbits. This problem turns out to be associated with thecontinuity breaking in a fixed point.
Viktor AvrutinIPVSUniversity of [email protected]
Laura GardiniUniversity of UrbinoDepartment of Economics and Quantitative [email protected]
Albert GranadosIPVS, University of [email protected]
Michael SchanzUniversity of Stuttgart, [email protected]
Iryna SushkoNational Academy of Sciences of Ukraine, Kiev, Ukraineira [email protected]
CP39
The Moving Average Transformation
We show that the moving average filter can be used as atool for smoothing non-differentiable flows. Viewing theaction of the filter as a change of variables these systemsare transformed to ODEs with continuous RHSs which en-joy a (slightly subtle) topological equivalence. This givesus a novel way to understand the complicated topology of adiscontinuous flows state space. It also provides a theoreti-cal justification for applying standard analysis to smootheddata when analysing time-series from a non-smooth sys-tem.
James L. HookUniversity of [email protected]
CP39
Analysis of the Dynamics Near a Degenerate Graz-ing Point for Rigid Impact Oscillators
In this work we study dynamics of one-dimensional oscil-lators with rigid fixed impacts. We introduce degenerategrazing points with some order of degeneracy as the pointswhere an orbit touches (grazes) tangent a rigid barrier withzero velocity and zero derivatives of the velocity up to someorder. Dynamics of the oscillator near the grazing point isinvestigated up to some extend.
Gheorghe Tigan, Jeroen Lamb, Oleg MakarenkovImperial College [email protected], [email protected],
DS11 Abstracts 117
CP42
Dynamically Reorganizing Neural Networks forStimulus Decorrelation
The neuronal network that performs the initial processingof odor information in the brain exhibits persistent rewiringeven in adult animals. We investigate how such a reorgani-zation allows this network to adapt to decorrelate represen-tations of similar stimuli. Using a simple model in whichthe survival of the neurons depends on their activity, we in-vestigate the influence of experimentally motivated nonlin-ear neuronal dynamics on the performance of the network.
Siu Fai ChowNorthwestern [email protected]
Hermann RieckeApplied MathematicsNorthwestern [email protected]
CP42
Synchronizing Distant Nodes: A Universal Classi-fication of Time-Delayed Networks
Stability of synchronization in delay-coupled networks ofidentical units generally depends in a complicated way onthe coupling topology. We show that for large couplingdelays synchronizability relates in a simple way to thespectral properties of the network topology. This allowsa universal classification of networks with respect to theirsynchronization properties and solves the problem of com-plete synchronization in networks with strongly delayedcoupling.
Valentin FlunkertTU [email protected]
Serhiy YanchukHumboldt University [email protected]
Thomas DahmsTU [email protected]
Eckehard SchollTechnische Universitat BerlinInstitut fur Theoretische [email protected]
CP42
Robustness of the Master Stability Function Ap-proach to Network Synhronization
We consider a typical experimental scenario for a set ofdynamical systems that are coupled through a network toachieve synchronization. We analyze a wide range of possi-ble deviations (mismatches) from nominal conditions thatmay affect simultaneously the individual units’ dynamics,the individual units’ output functions, and the couplinggains between the systems. We reduce the stability of thesynchronous solution in a master stability function form
and show that in the case of stability, the mismatches actas forcing terms that maintain the network in a state ofapproximate synchronization.
Francesco SorrentinoUniversita degli Studi di Napoli [email protected]
Maurizio PorfiriDept. of Mechanical, Aerospace and ManufacturingEngineeringPolytechnic [email protected]
CP43
Non-Gaussian Noise and its Effects on Scaling LawsNear Bifurcation Points
We study noise-induced switching of a system close tobifurcation parameter values where the number of stablestates changes. For non-Gaussian noise, the switching ex-ponent, which gives the logarithm of the switching rate,displays a non-power-law dependence on the distance tothe bifurcation point. This dependence is found for Pois-son noise. Even weak additional Gaussian noise dominatesswitching sufficiently close to the bifurcation point, leadingto a crossover in the behavior of the switching exponent.
Lora BillingsMontclair State UniversityDept. of Mathematical [email protected]
Ira B. SchwartzNaval Research LaboratoryNonlinear Dynamical Systems [email protected]
Mark I. DykmanDepartment of Physics and AstronomyMichigan State [email protected]
CP43
Stochastic Extinction in the Presence of DelayedFeedback
Extinction processes are stochastic events that occur inmany applications of finite populations such as reactionkinetics, population dynamics, and bio-chemical reactions.We consider the problem of stochastic extinction as a rareevent occurring in systems with delayed feedback. We de-rive a general formulation of the probability of extinction,and show analytically and numerically, how delay modu-lates the exponent of the mean time to extinction in sys-tems with both Gaussian and non-Gaussian noise.
Thomas W. CarrSouthern Methodist UniversityDepartment of [email protected]
Mark I. DykmanDepartment of Physics and AstronomyMichigan State [email protected]
Lora Billings
118 DS11 Abstracts
Montclair State UniversityDept. of Mathematical [email protected]
Ira B. SchwartzNaval Research LaboratoryNonlinear Dynamical Systems [email protected]
CP43
Set-based Corral Control in Stochastic DynamicalSystems
We consider the problem of stochastic prediction and con-trol in a time-dependent stochastic environment, such asthe ocean, where escape from an almost invariant re-gion occurs due to random fluctuations. We determinehigh-probability control-actuation sets using geometric andprobabilistic methods. These methods allow us to designregions of control that provide an increase in loitering timewhile minimizing the amount of control actuation. Ourmethods provide an exponential increase in loitering timeswith only small changes in actuation force. The result isthat the control actuation makes almost invariant sets moreinvariant.
Eric Forgoston, Lora Billings, Philip YeckoMontclair State UniversityDept. of Mathematical [email protected],[email protected], [email protected]
Ira B. SchwartzNaval Research LaboratoryNonlinear Dynamical Systems [email protected]
CP44
Workspace Estimation of Cooperating Robots afterJoint Failure
Remotely operating vehicles must have built-in robustnessto failure. We compute the post-failure workspace of twothree-link serial robots, where the failure of one robotsjoint is overcome by another arm grasping the broken link.We present an homotopy continuation algorithm for find-ing the optimal placement of such synergistic robot armsand the optimal grasp point on the final link of the brokenrobot. Finally, Monte-Carlo methods are used to estimatethe post-failure workspace.
Daniel A. Brake, Vakhtang PutkaradzeColorado State [email protected], [email protected]
Daniel J. BatesColorado State UniversityDepartment of [email protected]
Anthony MaciejewskiColorado State UniversityElectrical and Computer [email protected]
CP44
Equations with Advanced Arguments in a Segway
Model
A study about a very simple Segway model is presentedthat uses only one accelerometer to balance itself. The out-put of the controller incorporates both the angular positionand the angular acceleration of the Segway’s body. Differ-ent models of proportional-differential controllers are con-sidered. Analogue controllers with feedback delay resultin equations with advanced arguments (infinitely unstablesystem), while digital controllers provide stable balancing.The structure was manufactured and its stable motion isverified experimentally.
Tamas InspergerBudapest University of Technology and EconomicsDepartment of Applied [email protected]
Richard WohlfartBudapest University of Technology and [email protected]
Janos TuriUniversity of Texas at [email protected]
Gabor StepanBudapest University of Technology and EconomicsDepartment of Applied [email protected]
CP44
Identification of Nonlinear Characteristics Basedon Bistability in Delayed Model of Cutting
Nonlinear effects in cutting processes described by delay-differential equations result in parameters where chatteroccurs together with stable stationary cutting. A measure-ment is proposed to identify the width of this bi-stable zoneas function of chip thickness. The constant width of thisunsafe zone corresponds to the classical power law, whilea global maximum of the width of this zone may refer tothe existence of inflexion and/or asymptote in the cuttingforce characteristics.
Gabor StepanBudapest University of Technology and EconomicsDepartment of Applied [email protected]
Zoltan DombovariDepartment of Applied MechanicsBudapest University of Technology and [email protected]
Jokin MunoaIdeko Research Alliance IK4Danobat [email protected]
CP45
A Multicomponent Model for HeterogeneousBiofilms
Biofilms are common pathogenic bacterial communitiestypically existing in damp environments. A biofilm formswhen bacteria adhere to surfaces in a moist environment byexcreting a slimy, glue-like substance called the extracellu-
DS11 Abstracts 119
lar polymeric substance (EPS). Sites for biofilm formationinclude all kinds of surfaces: natural materials above andbelow ground, metals, plastics, medical implant materials,even plant and body tissues. Wherever you find a combi-nation of moisture, bacteria, nutrients and a surface, youare likely to find biofilms. Biofilms are a common cause ofchronic infection, and the costs associated with the treat-ment and prevention of biofilm related infections amountsto billions of dollars annually. We develop a tri-componentmodel for biofilm and solvent mixtures, in which the extra-cellular polymeric substance (EPS) network, bacteria andeffective solvent consisting of the solvent, nutrient, drugsetc. are modeled explicitly. The tri-component mixture isassumed incompressible as a whole while inter-componentmixing, dissipation, and conversion are allowed. A linearstability analysis is conducted on constant equilibria reveal-ing up to two unstable modes dependent upon the regimeof the model parameters. Computational simulations inone and two spatial dimensions are carried out to investi-gate the nonlinear dynamics of the EPS network, bacteriadistribution, drug and nutrient distribution in a channelwith and without shear.
Brandon S. Lindley, Qi WangUniversity of South [email protected], [email protected]
Tianyu ZhangMathematicsMontana State [email protected]
CP45
Stretch-Dependent Prolif-eration in a One-Dimensional Elastic ContinuumModel of Cell Layer Migration
A recently developed mathematical model of cell layer mi-gration based on an assumption of elastic deformation ofthe cell layer leads to a generalized Stefan problem. Themodel is extended to incorporate stretch-dependent pro-liferation, and the resulting PDE system is analyzed forself-similar solutions. The efficiency and accuracy of adap-tive finite difference and MOL schemes for numerical solu-tion are compared. We find a large class of assumptionsabout the dependence of proliferation on stretch that leadto traveling wave solutions.
Tracy L. StepienUniversity of [email protected]
David SwigonDepartment of MathematicsUniversity of [email protected]
CP45
Continuum Model of Collective Cell Migration inWound Healing and Colony Expansion
We derive a two-dimensional continuum mechanical modelof cell layer migration that is based on a novel assumptionof elastic deformation of the layer and incorporates theforce of lamellipodia, the adhesion of cells to the substrate,and the adhesion of cells to each other as well as cell prolif-eration and apoptosis. The evolution equations, which giverise to a Stefan type problem, are solved numerically usinga level set method. The model successfully reproduces data
from experiments on the contraction of an enterocyte celllayer during wound healing and the expansion of a colonyof MDCK cells.
David Swigon, Julia ArcieroDepartment of MathematicsUniversity of [email protected], [email protected]
Qi MiDepartment of Sports Medicine and NutritionUniversity of [email protected]
CP45
Modeling Compressive Nonlinearity of MammalianHearing
We introduce a cochlea model with outer hair cell somaticmotility as the active process. The model includes lon-gitudinal coupling through the outer hair and the basilarmembrane mechanics. We show that introducing inhomo-geneity in the feedback strength causes a radical increase ofthe response above the characteristic frequency. Moreover,combined with strong feedback inhomogeneity induces in-stability and oscillations that are associated with sponta-neous otoacoustic emissions.
Robert Szalai, Alan R. ChampneysUniversity of [email protected], [email protected]
Martin HomerUniversity of BristolEngineering Mathematics [email protected]
CP46
Models of Unidirectional Propagation in Heteroge-neous Excitable Media
In this talk nonlinear (ordinary and partial) differentialequation models of unidirectional propagation of the ac-tion potential in excitable media will be presented. In eachcase, the parameters are heterogeneous and unidirectionalpropagation arises from homogeneous initial data. Linearmodels with similar behavior are analyzed to find the crit-ical parameter regions over which unidirectional propaga-tion may occur. The model behavior is related to reentrantarrhythmias in cardiac tissue.
John G. AlfordTulane [email protected]
CP46
Bifurcation and Chaotic Dynamics in a CardiacModel with Memory
In predictions of arrhythmia, restitution is considered asthe most important predictor for electrical stability, al-though cardiac memory is also important. We report anovel prediction model consisting of two separate curves,which was used to simulate memory effect in addition torestitution. Results showed period-doubling bifurcations,conduction block; and importantly, higher order periodic-ity and chaos similar to ventricular fibrillation, followinga seeming return to stability, a feature not predicted by
120 DS11 Abstracts
other models.
Linyuan JingCenter for Biomedical EngineeringUniversity of [email protected]
Abhijit PatwardhanCenter for Biomdeical EngineeringUniversity of [email protected]
CP46
Spatiotemporal Dynamics of Calcium-Driven Al-ternans in Cardiac Tissue
We study a system of continuum coupled maps that modelsthe spatiotemporal dynamics of calcium-driven alternansin cardiac tissue. As calcium instability is increased, wefind a first transition from no alternans to smooth trav-eling waves, followed by a second novel bifurcation fromsmooth traveling waves to stationary patterns with discon-tinuous phase reversals. The transition is characterized byphase reversals that occur in a thin boundary layer whosethickness vanishes at the transition point.
Per Sebastian SkardalUniversity of Colorado at [email protected]
Juan G. RestrepoDepartment of Applied MathematicsUniversity of Colorado at [email protected]
Alain KarmaNortheastern UniversityCenter for Interdisciplinary Research in Complex [email protected]
CP47
Breaking the Symmetry of the Bimodal KuramotoSystem
In recent work, the complete bifurcation diagram for thebimodal Kuramoto system was reported. This system isa collection of phase oscillators with a bimodal frequencydistribution, connected via global mean-field coupling. Wecast this system as a pair of interacting populations in or-der to make clear a number of symmetries inherent in theoriginal system, and investigate the attractors and bifur-cations that arise as these symmetries are broken.
Ernest BarretoGeorge Mason UniversityKrasnow [email protected]
Bernard C. CottonGeorge Mason [email protected]
Paul SoGeorge Mason UniversityThe Krasnow [email protected]
CP47
A Transport Equation for Pulse-Coupled Phase Os-cillators and a Lyapunov Function for Its GlobalAnalysis
We consider the continuous limit of an infinite number ofpulse-coupled phase oscillators. Under monotonicity as-sumptions on the phase response curve of the oscillators,we introduce a Lyapunov function that provides a globalstabilty analysis of the asynchronous (uniform flux) solu-tion. The proposed Lyapunov function has a natural in-terpretation of total variation distance between densities.The result is applied to various models, including the con-tinuous limit of LIF oscillators (Peskin model).
Alexandre Mauroy
University of Liege / Montefiore Institute (B28)Departement of Electrical Engeneering and [email protected]
Rodolphe SepulchreUniversity of [email protected]
CP47
What Does Thermodynamic Limit Tell Us AboutChimera States?
Chimera states are recently discovered spatio-temporalpatterns with a surprising dynamical behavior, where aspatially homogeneous system of identical oscillators withidentical coupling topologies self-organizes into a spatiallyintermittent pattern of regions with different synchronousbehavior, e.g., with coherent and incoherent motion. Themacroscopic dynamics of the chimera state can be ex-plained to a large extent by considering the correspondingthermodynamic limit equation. However, the bifurcationanalysis of this equation requires a delicate interpretationas soon as we go back to a finite size system of coupledoscillators.
Oleh Omel’chenkoWeierstrass [email protected]
Matthias WolfrumWeierstrass Institute for Applied Analysis and [email protected]
CP48
Multiple Phase Locked States in Half-Center Os-cillators
We study half-center networks, formed by two endoge-nously bursting neurons, with fast non-delayed inhibitoryconnections. We find that fast reciprocal inhibition, knownto facilitate anti-phase bursting, can also produce multipleco-existent phase locked states, including stable in-phasebursting. We demonstrate that this phenomenon is generalby analyzing different models of fast synapses and burstingcells: leech heart inter-neurons, Sherman pancreatic betacells and Purkinje neurons. We discuss implications forlocomotion and memory storage.
Sajiya Jalil, Igor BelykhDepartment of Mathematics and StatisticsGeorgia State University
DS11 Abstracts 121
sja [email protected], [email protected]
Andrey ShilnikovNeuroscience Institute and Department of MathematicsGeorgia State [email protected]
CP48
Crawling Without CPG: A NeuromechanicalModel
Locomotion of soft bodied animals is usually achieved bythe propagation of contraction/extension waves along thebody. The generation of these rhythmic movements hasbeen classically attributed to pattern generation in thenervous systems, but new experimental results seems tocontradict this hypothesis. Here we discuss an alternativemechanism where the mechanical properties of the bodyand the substrate are coupled with simple neuronal dy-namics to achieve coordination. Analytical and numericalresults are presented, along with a qualitative comparisonwith data.
Paolo Paoletti, L. MahadevanSchool of Engineering and Applied SciencesHarvard [email protected], [email protected]
CP48
A Mechanism of Abrupt Transitions Between Fir-ing Frequency Regimes in Entorhinal stellate Cells
In this work we investigate the biophysical and dynamicmechanism responsible for the abrupt (threshold-like) tran-sition between theta (4 - 10 Hz) and hyperexcitable ( 60Hz) firing frequencies in stellate cells (SCs) as the resultof an increase in the level of recurrent excitation. Abrupttransitions are not observed in isolated cells as the resultof increases in the levels of tonic drive. Differently fromother mechanisms of hyper-excitability, there is no bista-bility involved.
Horacio G. RotsteinNew Jersey Institute of [email protected]
Tilman KisperskyBrandeis [email protected]
John Whitedepartment of BioengineeringThe University of [email protected]
CP48
Astrocyte Mediated Modifications in FunctionalNeuronal Network Strucutre
We used a novel clustering algorithm to detect changes inneuronal dynamics elicited by modifications in astrocyticdensity in cultured neuronal networks. The networks in thehigh glial group show an increase in global synchronizationas the cultures age, while those in the low glial group re-main locally synchronized. We additionally quantify theoverall synchronization levels present in the cultures andshow that the total level of synchronization in the highglial group is stronger than in the low glial group. These
results indicate an interdependence between the glial andneuronal networks present in dissociated cultures.
Sarah FeldtUniversity of [email protected]
Jane Wang, Elizabeth ShtrahmanApplied PhysicsUniversity of [email protected], [email protected]
Eva OlariuNeuroscience ProgramUniversity of [email protected]
Michal ZochowskiBiophysicsUniversity of [email protected]
CP49
Synchronization of Spatiotemporal Chaos inRayleigh-Benard Convection
Synchronization of spatiotemporal chaos in Rayleigh-Benard convection is studied numerically by imposing thetime-dependent boundary conditions from a principal do-main onto an initially quiescent target domain. The twoconvection layers are considered synchronized when theyexhibit the same chaotic dynamics. We are interested inidentifying a synchronization length scale to quantify thesize of chaotic element and in its relationship with thechaotic length scale determined from computations of thefractal dimension.
Alireza KarimiDepartment of Engineering Science & MechanicsVirginia [email protected]
Mark PaulDepartment of Mechanical EngineeringVirginia [email protected]
CP49
Designing a Computing System Based on a ChaoticDynamical System by Use of Numerical Analysis
The complex dynamics of chaotic systems can performcomputation. Previously the exact dynamical equationsof the chaotic system were used to design a computing sys-tem. We demonstrate a chaos computing system can alsobe designed by having only a time series from the underly-ing chaotic system. We numerically extract unstable peri-odic orbits and their eigenvalues from the time series, andthen determine the functionality of underlying dynamicalsystem and its robustness in doing computation.
Behnam KiaSchool of Electrical, Computer and Energy Engineering,ASUSchool of Biological and Health Systems Engineering,[email protected]
122 DS11 Abstracts
Mark Spano, William DittoSchool of Biological and Health Systems EngineeringArizona State [email protected], [email protected]
CP49
Chaotic Properties in Violin Sounds
Violin sounds show complicated twisted orbits which looklike strange attractors. We found that violin sounds havedeterminism beyond pseudo-periodicity with positive Lya-punov exponents. Poincare sections of violin sounds showcomplicated state transitions. Our results show that violinsounds are likely to be of deterministic chaos.
Masanori ShiroUniversity of [email protected]
Yoshito HirataInstitute of Industrial ScienceThe University of [email protected]
Kazuyuki AiharaJST/University of Tokyo, JapanDept of Mathematical [email protected]
CP49
Length Scale of Interaction in SpatiotemporalChaos
Extensive systems have no long scale correlations and be-have as a sum of their parts. Various techniques are in-troduced to determine a characteristic length scale of in-teraction beyond which spatiotemporal chaos is extensivein reaction-diffusion networks. Information about networksize, boundary condition or abnormalities in network topol-ogy gets scrambled in spatiotemporal chaos, and the atten-uation of information provides such characteristic lengthscales.
Renate A. Wackerbauer, Dan StahlkeUniversity of Alaska FairbanksDepartment of [email protected], [email protected]
CP50
Chaotic Ionization of Bidirectionally Kicked Ryd-berg Atoms
A highly excited quasi one-dimensional Rydberg atom ex-posed to periodic alternating external electric field pulsesexhibits chaotic behavior. The ionization of this system isgoverned by a homoclinic tangle attached to a fixed pointat infinity. We present and explain the results from twoexperiments designed to probe the structure of the phasespace turnstile. The first experiment focuses on observinga step-function-like behavior of the ionization fraction as afunction of the strength and period of the applied electricfield pulses. The second experiment observes the periodicdips in survival probability as a function of the position ofthe starting electron ensemble in phase space. Both exper-iments highlight the important role phase space turnstilesplay in interpreting the ionization process.
Korana Burke
Kevin A. MitchellUniv of California, MercedSchool of Natural [email protected]
Barry Dunning, Brendan Wyker, Shuzhen YeRice [email protected], [email protected], [email protected]
CP50
Quantum Scars in Graphene Billiards
The quasiparticle of graphene behaves like chiral, masslessDirac Fermions in the low energy range, thus the concen-trations of wave functions about classical unstable periodicorbits provides a probe for relativistic quantum scars. Anumber of issues, e.g., geometric symmetry of the billiard,small perturbations, effect of magnetic field, etc., will bediscussed. Relation with conductance fluctuation and lo-cal magnetic moment generation for corresponding opengraphene quantum dots will also be discussed.
Liang HuangDepartment of Electrical EngineeringArizona State University, Tempe, Arizona 85287, [email protected]
Ying-Cheng LaiArizona State UniversityDepartment of Electrical [email protected]
Celso GrebogiKing’s CollegeUniversity of [email protected]
David FerryArizona State [email protected]
CP50
A New Experimental Probe for Investigating theDynamics of Relativistic Electrons in StorageRings
In a storage ring, relativistic electron bunches follow aclosed orbit, during typically several hours. When thebunch charge exceeds a threshold, spatio-temporal instabil-ities occur, leading to rapidly evolving patterns. Howeverthese patterns are usually not accessible to observations.Here we use an alternate method, consisting to study thebunch dynamics when it experiences perturbations fromlaser pulses. The results are compared to numerical sim-ulations and analytic approximations of the underlyingFokker-Planck-Vlasov model.
Christophe Szwaj
Universite de Lille (France)Laboratoire [email protected]
DS11 Abstracts 123
CP50
Quantum Chaotic Scattering in Graphene Systems
We investigate the transport fluctuations in both non-relativistic quantum dots and graphene quantum dots withboth hyperbolic and nonhyperbolic chaotic scattering dy-namics in the classical limit. We find that nonhyperbolicdots generate sharper resonances than those in the hyper-bolic case. Strikingly, for the graphene dots, the resonancestend to be much sharper. This means that transmission orconductance fluctuations are characteristically greatly en-hanced in relativistic as compared to non-relativistic quan-tum systems.
Rui Yang, Liang HuangSchool of Electrical, Computer, and Energy EngineeringArizona State University, Tempe, AZ 85287, [email protected], [email protected]
Ying-Cheng LaiArizona State UniversityDepartment of Electrical [email protected]
Celso GrebogiKing’s CollegeUniversity of [email protected]
CP51
Dissipative 3D Vortices, Their Filaments’ Tensionand Response Functions
We consider a parametric region in the FitzHugh-Nagumomodel where stable alternative scroll wave solutions withdifferent periods exist. We use asymptotics based on re-sponse functions to predict filament tension of the scrolls.We find that alternative scrolls can have filament tensionsof opposite signs. We confirm these predictions by directsimulations, and also show conversion of alternative vor-tices into each other by uniform shocks, interaction withboundaries, and curvature of scroll filaments.
Irina BiktashevaUniversity of [email protected]
Dwight BarkleyUniversity of WarwickMathematics [email protected]
Vadim N. BiktashevUniversity of Liverpool, [email protected]
ANDREW J. FoulkesUniversity of Manchester, [email protected]
CP51
Collective Movement of Animals and the Emer-gence of Territorial Patterns
We formulate the problem of animal territoriality as a formof collective movement of wandering animals that continu-ously deposit scent marks and avoid the locations recentlymarked by other conspecifics. We show that the dynamics
of each territory, i.e. the area delimited by the locationswhere the scent marks of neighbours are present, becomesa 2D exclusion process, and that only two parameters, pop-ulation density and the active scent time, control how ter-ritorial patterns emerge.
Luca GiuggioliUniversity of BristolBristol Centre for Complexity [email protected]
Jonathan Potts, Stephen HarrisUniversity of [email protected], [email protected]
CP51
A New Type of Relaxation Oscillations in a Modelfor Enzyme Reactions
We present a geometric analysis of a new type of relax-ation oscillations in a model of an enzyme reactions cas-cade. The model developed by A. Goldbeter describes themitosis part of the cell division cycle in eukaryotes. Werewrite the model as a three dimensional singularly per-turbed system and use a combination of topological andgeometric methods (Conley index theory and the blow-upmethod) to prove the existence of a periodic orbit in themodel.
Ilona KosiukMPI MiSInselstrasse 22, 04103 Leipzig [email protected]
Peter SzmolyanInstitut for Applied Mathematics and Numerical AnalysisVienna University of [email protected]
CP51
Stability Analysis of Pulsative Solutions of Legiato-Lefever Equation
We study the stability and bifurcation of steady states fora certain kind of a damped driven nonlinear Schrodingerequation with cubic nonlinearity and detuning term in onespace dimension, mathematically in a rigorous sense. Itis known by numerical simulation that the system showslots of coexisting spatially localized structures as a resultof subcritical bifurcation. Since the equation does not havevariational structure, unlike the conservative case, we can-not apply a variational method capturing the ground state.Hence, we analyze the equation from a viewpoint of bifur-cation theory. In the case of a finite interval, we prove thefold bifurcation of nontrivial stationary solutions aroundthe codimension two bifurcation point of the trivial equi-librium by exact computation of fifthorder expansion ona center manifold reduction. In addition, we analyze thesteady-state mode interaction and prove the bifurcation ofmixed-mode solutions, which will be a germ of localizedstructures on finite interval. Finally, we study the corre-sponding problem on the entire real line by use of spatialdynamics. We obtain a small dissipative soliton bifurcatedadequately from the trivial equilibrium. In additon, we willtoal about some results in two space dimensional domain.References [1] L. A. Lugiato and R. Lefever, Spatial Dissi-pative Structures in Passive Optical Systems, Phys. Rev.Lett., 58 (1987), 22092211. [2] T. Miyaji, I. Ohnishi andY. Tsutsumi, Bifurcation analysis to the Lugiato-Lefever
124 DS11 Abstracts
equation in one space dimension, Physica D, 239 (2010),20662083. [3] M. Golubitsky, I. Stewart and D. G. Scha-effer, Singularities and Groups in Bifurcation Theory II,Applied Mathematical Sciences, 69, Springer- Verlag, NewYork (1988).
Tomoyuki MiyajiResearch Institute for Mathematical Sciences,Kyoto [email protected]
Isamu OhnishiHiroshima Universityisamu [email protected]
Yoshio TsutsumiDepartment of Mathematics, Graduate School of ScienceKyoto [email protected]
CP52
Control of An Anaerobic Digester Through NormalForm of Fold Bifurcation
Nonlinear dynamics and bifurcations are ubiquitous in en-gineering systems. Computing the corresponding normalform of a bifurcation close to an operation point, and tak-ing this model as the nominal plant, we design a nonlinearcontrol which takes advantage of the precise bifurcationscenario. This general method is applied to a 4-dimensionalanaerobic digester with adaptive control, which showssaddle-node and transcritical bifurcations. Our methodhas low control effort and error and faster convergence rate.
Gerard Olivar, Fabiola AnguloDepartment of Electrical and Electronics EngineeringUniversidad Nacional de Colombia, sede [email protected], [email protected]
Alejandro RinconUniversidad Nacional de Colombia, sede [email protected]
CP52
Microwave Chaotic Oscillators UsingTime-Delayed Feedback
We describe a nonlinear microwave circuit that uses time-delayed feedback to a voltage-controlled microwave os-cillator. We present experimental measurements of thebifurcation diagram, showing dynamical behaviors rang-ing from periodic to chaotic, depending on the feedbackstrength. When two such systems were bidirectionally cou-pled, we observed envelope and phase synchronization be-tween them. The phase synchronization was investigatedby applying the Hilbert transform to the measured mi-crowave signals generated by the two synchronized systems.
Hien DaoChemical Physics ProgramUniversity of Maryland- College parkhiendao@umd,edu
John RodgersInstitute for Research in Electronics and Applied PhysicsUniversity of Maryland- College [email protected]
Thomas E. MurphyUniversity of Maryland, College ParkDept. of Electrical and Computer [email protected]
CP52
Swarm Clustering Arising from Consensus Algo-rithms
The rendezvous problem is to provide a distributed algo-rithm that causes a large number of agents to meet atthe same location, perhaps under severe communicationconstraints. If there is a fixed, connected communicationnetwork, an averaging algorithm solves the problem; how-ever, if the network changes in time, the averaging algo-rithm will produce localized clusters of agents. We pro-vided an efficient computational framework to determinethe location and relative sizes of clusters in an arbitrarytwo-dimensional environment with a random initial distri-bution of agents.
Bruce RogersDuke [email protected]
CP52
Effect of Micro Structure Anisotropy on Dynami-cally Self Assembled Two Dimensional Structures
We study dynamical self assembly (SA) process in twodimensional space from a topological perspective. Eachmicro-structure is modeled as an n-fold symmetric diskwith distinct sites of attachment. Every pair of active siteinteracts with a short range potential. We introduce theconcept of local minimal structures to study all possiblelocal SA configurations. Our simulations suggest that theedge count generated between a specific pair of active sitesis a good observable to quantify topological dominance ofone assembly rule over another. We offer a dynamical andthermodynamical insight into the reasons for this.
Gunjan ThakurDepartment of Mechanical EngineeringUniversity of California at Santa [email protected]
Igor MezicUniversity of California, Santa [email protected]
CP53
Stability Analysis for Periodic Waves of a FourthOrder Beam Equation
We consider the periodic waves of a fourth order BeamEquation. We use constrained minimization technique toshow the existence of such solutions. We study the spec-trum of the linearized operator both analytically and nu-merically. Based on the linearly unstable modes found inthe numerics, we propose a method to show nonlinear in-stability.
Milena StanislavovaUniversity of Kansas, LawrenceDepartment of [email protected]
Aslihan Demirkaya
DS11 Abstracts 125
University of Kansas, [email protected]
CP53
Bifurcation of Hyperbolic Planforms in a Relationwith a Model of Texture Perception
Motivated by a model for the perception of textures bythe visual cortex in primates introduced by Chossat andFaugeras (Hyperbolic planforms in relation to visual edgesand textures perception, Plos. Comp. Bio. 2009) andthen theoretically studied in Faye-Chossat etal (Some the-oretical results for a class of neural mass equation, ArXiv2010, submitted to the Journal of Mathematical Neuro-science), we analyse the bifurcation of periodic patternsfor integro-differential equations describing the state of asystem defined on the space of structure tensors, whenthese equations are further invariant with respect to theisometries of this space. We show that the problem re-duces to a bifurcation problem in the hyperbolic plane D(Poincare disc). We apply the machinery of equivariant bi-furcation theory (see Chosst-Faye etal, Bifurcation of hy-perbolic planforms, Journal of Nonlinear Science 2010) inorder to classify all possible H-planforms satisfying the hy-potheses of the Equivariant Branching Lemma. We studyseparately the 4 dimensional cases as no simple reductioncan be made.
Gregory FayeINRIA Sophia Antipolis [email protected]
Pascal ChossatINRIA, Sophia Antipolis, CNRS, ENS Paris, FranceCNRS and University of Nice [email protected]
Olivier FaugerasINRIA Sophia Antipolis [email protected]
CP53
Anomalous Thermalization of Nonlinear Wave Sys-tems
We investigate both theoretically and experimentally thehamiltonian nonlinear propagation of partially-coherentoptical waves which is ruled by NLS-type equations. Us-ing wave-turbulence theory, we show that the existenceof degenerate resonance conditions leads to an irreversibleevolution of the wave systems towards specific equilibriumstates of a fundamental different nature than the usualthermodynamic equilibrium distribution; in particular, thisnew thermodynamic equilibrium does not respect the ex-pected energy equipartition among the modes.
Pierre SuretUniversite de Lille [email protected]
Claire Michel, H.R. Jauslin, A. PicozziUniversite de [email protected], [email protected], [email protected]
Stephane RandouxUniversite de Lille [email protected]
CP54
Modelling and Parameters Indentification of Per-manent Synchronous Motors
This paper deals with a dynamic estimator for fully au-tomated parameters indentification of permanent magnetthree-phase synchronous motors. High performance appli-cation of permanent magnet synchronous motors (PMSM)is increasing. PMSM models with accurate parameters aresignificant not only for precise control system designs butalso in traction applications. Acquisition of these param-eters during motor operations is a challenging task due tothe inherent nonlinearity of motor dynamics. This paperproposes parameters estimator technique for PMSMs. Adynamic estimator is shown. The estimator uses the mea-surements of input voltage, current and mechanical angularvelocity of the motor, the estimated winding inductance,and resistance to identify the amplitude of the linkage flux.The presented technique is generally applicable and couldbe used also for the estimation of mechanical load and forother types of electrical motors, as well as for other dy-namic systems with nonlinear model structure. Throughsimulations of a synchronous motor used in automotive ap-plications, this paper verifies the effectiveness of the pro-posed method in identification of PMSM model parame-ters and discusses the limits of the found theoretical andthe simulation results.
Paolo MercorelliUniversity of Applied Sciences [email protected]
CP54
Dynamical Systems in Circuit Designers Eyes
Recent developments in communication and computer cir-cuits make the dynamical system theory more than everimportant to EE designers. At the same time the lan-guages of these two worlds (design and DS theory) remainmutually incomprehensible. This paper aims at diminish-ing the gap by describing some fairly simple but importantcircuits from both points of view, in particular it presentssuccesses and limits of state space analysis and presentssome open design problems.
Michal [email protected]
CP54
Satisfiability of Elastic Demand in the Smart Grid
We study a stochastic model of electricity production andconsumption where appliances are adaptive and adjusttheir consumption to the available production, by delayingtheir demand and possibly using batteries. The model in-corporates production volatility due to renewables, ramp-up time, uncertainty about actual demand versus plannedproduction, delayed and evaporated demand due to adap-tation to insufficient supply. We study whether thresholdpolicies stabilize the system. The proofs use Markov chaintheory on general state space.
Dan-Cristian [email protected]
Jean-Yves Le Boudec
126 DS11 Abstracts
EPFL-I&[email protected]
CP54
Chaos Control in a Transmission Line Model
In a transmission line oscillator a linear wave travels alonga piece of cable,the transmission line, and interacts withterminating electrical components. Diodes are integratedinto almost all electronic devices as a means of protect-ing the logic circuits from destructive outside signals andhigh-voltage discharges. In the simple network model thatwe will present, we show nonlinear and chaotic effects as-sociated with diodes that if transmitted into the primarycircuitry will disrupt or possibly damage the device .
Ioana A. TriandafNaval Research LaboratoryPlasma Physics [email protected]
CP55
Forecasting Bifurcations for Sensing Applications
Characterizing bifurcations after they occur is currentlypossible by a variety of techniques. However, forecast-ing bifurcations (i.e. predicting them before they occur)is a significant challenge and an important need in severalfields, including sensing. A few existing approaches de-tect bifurcations before they occur by exploiting the criti-cal slowing down phenomenon. However, the perturbationsneeded in those approaches are limited to very small lev-els and that represents a significant drawback. Large lev-els of perturbation have not been used mainly because ofa lack of an adequate formulation robust to experimentalnoise. This presentation provides such a needed formu-lation, and discusses an approach to predict bifurcationsmore accurately, especially when the dynamics is far fromthe bifurcation. Both numerical and experimental resultsare presented to demonstrate the proposed technique andshow its advantages over other prediction methods.
Bogdan I. EpureanuDepartment of Mechanical EngineeringUniversity of MIchigan - Ann [email protected]
CP55
Unfolding the Catastrophe of the Elastic Web ofLinks
An axially compressed rod with infinite bending and axialstiffness and finite shear stiffness has one critical point onits trivial equilibrium path. The elastic web of links withN columns can be used as a discrete model of this rod. Ithas an (N − 1)-tuple cusp catastrophe at its bifurcationpoint along the trivial equilibrium path. We will show thediscrete model, and how varying shear stiffness or a smallbending stiffness disturbs the bifurcation diagram of thediscrete system (i.e. the (N − 1)-tuple cusp catastropheunfolds to lower order cusp catastrophes).
Robert K. NemethBudapest University of Technology and EconomicsDepartment of Structural [email protected]
Attila G. Kocsis
Department of Structural MechanicsBudapest University of Technology and [email protected]
CP55
Heteroclinic Breakdown Beyond All Orders inGeneric Analytic Unfoldings of the Hopf-Zero Sin-gularity
A classical problem in the study of the Hopf-zero bifurca-tion, is to obtain Shilinkov bifurcations in its unfoldings.The first step is to prove that the heteroclinic orbit be-tween the two saddle-focus type equilibrium points, whichexists in the normal form up to any order, breaks down.This breakdown makes possible the existence of homoclinicorbits to the equilibrium points. In this talk, we showthat this splitting is a ”beyond all orders” phenomenon, inthe sense that it is exponentially small with respect to theperturbative parameter. Moreover, we provide a formulawhich measures the distance between the correspondingstable and unstable one dimensional manifolds. We showthat, for generic unfoldings, this formula does not agreewith the one provided by the classical Melnikov approach.Moreover, the condition which guarantees the splitting ofthe heteroclinic connection depends of the full jet of the un-folding and can not be checked using classical perturbationtheory.
Tere M. SearaUniv. Politecnica de [email protected]
Immaculada Baldoma, Oriol CastejonUniversitat Politecnica de [email protected], [email protected]
CP55
Dynamic Stability of Rigid Objects with FrictionalSupports
Various engineering structures and quasi-static robots aremodelled by rigid bodies with frictional contacts. Little isknown about the stability of such objects against dynamicperturbations, due to their nonlinear, and discontinuousresponses. We present novel sufficient local stability con-ditions for planar objects on slopes, demonstrate some in-triguing properties of the exact stability condition, discussthe role of impact rules, and propose a simple and robustalgorithm to stabilize three-dimensional objects on arbi-trary terrains.
Peter L. VarkonyiBudapest University of Technology and [email protected]
David GontierEcole Normale Superieure, [email protected]
Joel W. BurdickCalifornia Institute of TechnologyDepartment of Mechanical [email protected]
MS1
Langmuir Circulation, Mixing, and Instabilities in
DS11 Abstracts 127
the Ocean Surface Boundary Layer
The wind- and surface-wave-driven oceanic boundary layer(BL) is the sight of intense, episodic mixing events me-diated by fluid dynamical instability processes. On thescale of the O(100) meter deep BL, a primary mechanismfor vertical transport and mixing is Langmuir circulation(LC). Over scales ranging from 1-10 kilometers (the “sub-mesoscales”), upper ocean dynamics are dominated by in-ternal waves and lateral density fronts, which themselvesare susceptible to other instability processes (e.g. symmet-ric instabilities). Here, a combination of linear stabilitytheory, numerical simulations, and multiscale asymptoticanalysis is used to investigate the oft-neglected impact ofLC on submesoscale mixing and transport phenomena.
Greg ChiniProgram in Integrated Applied MathematicsUniversity of New [email protected]
Ke LiUniversity of [email protected]
Zhexuan Zhang, Ziemowit MalechaUniversity of New [email protected], [email protected]
Keith JulienApplied MathematicsUniversity of Colorado, [email protected]
MS1
Optimal Stirring for Passive Scalar Mixing
We address the challenge of optimal incompressible stirringto mix an initially inhomogeneous distribution of passivetracers. As a measure for mixing we adopt the H−1 normof the scalar fluctuation field. This ’mix-norm’ is equivalentto (the square root of) the variance of a low-pass filteredimage of the tracer concentration field, and is a useful gaugeeven in the absence of molecular diffusion. We show thatthe mix-norm’s vanishing as time progresses is evidence ofthe stirring flow’s mixing property in the sense of ergodictheory. For the case of a periodic spatial domain with aprescribed instantaneous energy or power budget for thestirring, we determine the flow field that instantaneouslymaximizes the decay of the mix-norm, i.e., the instanta-neous optimal stirring — when such a flow exists. Whenno such ’steepest descent’ stirring exists, we determine theflow that maximizes that rate of increase of the rate ofdecrease of the norm. This local-in-time stirring strategyis implemented computationally on a benchmark problemand compared to an optimal control approach utilizing arestricted set of flows.
Charles R. DoeringUniversity of MichiganMathematics, Physics and Complex [email protected]
Zhi LinUniversity of MinnesotaInstitute for Mathematics& Its [email protected]
Jean-Luc ThiffeaultDept. of MathematicsUniversity of Wisconsin - [email protected]
MS1
Internal Trapping of Bodies, Plumes and Jets in aStratified Fluid: A Theoretical and ExperimentalStudy
The motion of bodies and fluids moving through a stratifiedbackground fluid arises naturally in the context of carbon(marine snow) settling in the ocean, as well as less natu-rally in the context of the recent gulf oil spill. The detailsof the settling rates may play a role in assessing the roleof the ocean in the earth’s carbon cycle. In this lecture,we look at phenomena associated with falling spheres instratified fluids, and in particular focus upon the criticalparameters setting when transient sphere levitation is pos-sible. We present detailed theory for single bodies at bothinviscid and viscous extremes, and overview closure mod-els for handling the jet and plume cases. this work is jointwith Roberto Camassa
Richard McLaughlinUNC Chapel [email protected]
MS1
Topological Detection of Lagrangian CoherentStructures
In many applications, particularly in geophysics, we oftenhave fluid trajectory data from floats, but little or no infor-mation about the underlying velocity field. The standardtechniques for finding transport barriers, based for exampleon finite-time Lyapunov exponents, are then inapplicable.However, if there are invariant regions in the flow this willbe reflected by a ‘bunching up’ of trajectories. We showthat this can be detected by tools from topology.
Jean-Luc ThiffeaultDept. of MathematicsUniversity of Wisconsin - [email protected]
Michael AllshouseDept. of Mechanical EngineeringMassachusetts Institute of [email protected]
MS2
Many Body Quantum Chaos in Atomic Bose-Einstein Condensates in a Few Well System
We will investigate signatures of complex transport in thequantum (counting and occupation) statistics, of drivenatomic Bose - Einstein Condensates (BEC) in few well op-tical lattices with multi -path topologies. Then, we willcoupled these systems with infinite leads and study theirdecay and scattering properties. Theoretical tools, bor-rowed from quantum chaos, such as semiclassics, scalingtheory and Random Matrix modeling will be applied, andwill allow us to derive predictions beyond those providedby mean-field theories.
Tsampikos KottosWesleyan University
128 DS11 Abstracts
Dept. of [email protected]
MS2
Relativistic Quantum Chaos in Graphene Systems
Existing works on quantum chaos are concerned almost ex-clusively with non-relativistic quantum systems describedby the Schrodinger equation, where the dependence of theparticle energy on the momentum is quadratic. A naturalquestion is whether phenomena in non-relativistic quantumchaos can occur in relativistic quantum systems describedby the Dirac equation, where the energy-momentum rela-tion is linear. The speaker will discuss recent results fromhis group on relativistic quantum chaos in graphene sys-tems: energy-level statistics, scars, chaotic scattering, andstochastic resonance.
Ying-Cheng LaiArizona State UniversityDepartment of Electrical [email protected]
MS2
Theory of Chaos Regularization of Tunneling
The previous talk reported the striking numerical discoverythat fluctuations of tunneling rates in quantum-dot-typegeometries can be orders of magnitude smaller for chaoticsystems as compared to otherwise similar integrable sys-tems, even in though, when the fluctuations are averagedover, the two give the identical results. In this talk wegive theory explaining these interesting findings, and wetest our predictions by quantitative comparison with thenumerical results.
Edward OttUniversity of MarylandInst. for Plasma [email protected]
Ming Jer Lee, Thomas M. AntonsenUniversity of [email protected], [email protected]
Louis Pecora, Dong-Ho Wu, Hoshik LeeU.S. Naval Research [email protected], [email protected],[email protected]
MS2
Chaos Regularization of Quantum Tunneling Rates
We show that quantum tunneling rates are effected greatlyby the shape of the potential wells. Shapes that have reg-ular classical behavior have tunneling rates which can varyby several orders of magnitude. Well shapes that have clas-sically chaotic behavior have narrower ranges of tunnelingrates by an order of magnitude or more. This change comesfrom destabilization of periodic orbits in the regular wellsthat produce the largest and smallest tunneling rates.
Louis M. PecoraNaval Research [email protected]
MS3
Exact Order Parameter Theory for Patterns andMode Interactions in Driven Granular Systems
Starting from the continuum equations of rapid granularflows, we derive the Landau equation to describe nonlin-ear patterns in granular shear flows using both amplitude-expansion and center-manifold reduction techniques. Un-like previous works, the present order-parameter equationis exact in the sense that there are no fitting parameters.We will discuss the predictions of our nonlinear theory tomimic various patterns as well as its extension for modeinteractions in driven granular systems.
Meheboob Alam, Priyanka ShuklaJNCASR, [email protected], [email protected]
MS3
Analysis of Emerging Structures in Particle Models
The macroscopic behaviour of microscopically defined par-ticle models are investigated by equation-free techniques.For two examples, pedestrian flow and traffic flow, a nu-merical bifurcation analysis of macroscopic quantities de-scribing the structure formation in the particle models wasperformed. The pedestrian flow shows the emergence ofan oscillatory pattern of two crowds targeting in oppositedirections and passing a narrow door. The traffic flow on asingle lane highway shows traveling waves of high densityregions.
Jens StarkeTechnical University of DenmarkDepartment of [email protected]
Rainer BerkemerAKAD Hochschule [email protected]
Olivier CorradiTechnical University of [email protected]
Poul G. HjorthTechnical Univ of DenmarkDepartment of [email protected]
MS3
A Primer of Swarm Equilibria
We study equilibria of swarming organisms subject to ex-ogenous and endogenous forces. Beginning with a discretedynamical model, we derive a variational description of thecorresponding continuum population density and find ex-act solutions for equilibria. Typically, these are compactlysupported with jump discontinuities or δ-concentrationsat the group’s edges. We apply our methods to locustswarms, which are observed in nature to consist of a con-centrated population on the ground separated from an air-borne group.
Chad M. TopazMacalester [email protected]
Andrew J. Bernoff
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Harvey Mudd CollegeDepartment of [email protected]
MS3
Accelerating Agent-Based Computation of Com-plex Urban Systems
Despite its popularity, agent-based modeling is criticallylimited by barriers that constrain its usefulness as an ex-ploratory tool. This is particularly problematic for agent-based models of complex urban systems in which simula-tion of macroscopic phenomena such as sprawl may takeenormous computing time. We introduce two schemes foraccelerating simulation of urban sprawl from local driversof urban growth. The schemes can significantly speed upthe complex urban simulations, while maintaining faithfulrepresentation of original models.
Yo ZouPrinceton [email protected]
Roger GhanemUniversity of Southern CaliforniaAerospace and Mechanical Engineering and [email protected]
MS4
Temporal Features in Insect Olfactory System: Dy-namics on a Directed Graph
We study temporal properties of the olfactory system us-ing a network model, reduced to dynamics on a directedgraph. We find the features of ”dynamic clustering” (inwhich subsets of cells join in and drop out of synchronousclusters); the divergence of representation of similar odorsover time (differentiation) and the convergence of repre-sentations of other odors (generalization) in transients andattractors of network dynamics. We explore numericallytheir dependence on network parameters.
Alla BorisyukUniversity of UtahDept of [email protected]
MS4
Eigenvalues of Graphs
Graph theory is the study of networks. To a graph, one canassociate various matrices such as adjacency matrix, Lapla-cian or normalized Laplacian matrix. In many situations,the only way we can study key combinatorial parametersof graphs such as edge-distribution, connectivity or expan-sion, is by using the eigenvalues of these matrices. In thistalk, I will describe some of the connections between thestructure of graphs and their eigenvalues.
Sebastian CioabaUniversity of Delaware at [email protected]
MS4
Excitable Networks: Spontaneous Spiking, Syn-
chrony, and Waves
We study electrically coupled networks of excitable neuronsforced by small noise. Using the center manifold reduction,techniques for randomly perturbed dynamical systems, andelements of algebraic graph theory, we derive a variationalproblem, which provides a clear geometric picture of thenetwork dynamics. In particular, we describe the evolutionof spontaneous patterns starting from uncorrelated activityfor very weak coupling, and progressing through formationof clusters, and waves, to complete synchrony for strongercoupling.
Georgi S. MedvedevDrexel UniversityDepartment of [email protected]
MS4
Collective Decision Making in the Two-AlternativeForced-Choice Task: A Coupled Stochastic Differ-ential Equations Model
This talk investigates the effect of coupling among individ-uals in a collective decision-making scenario, in which thetask is to correctly identify a (noisy) stimulus between twoknown alternatives. Multiple decision-making units, eachrepresented by a Drift-Diffusion Model (DDM), accumu-late evidence toward a decision and share evidence witha possibly limited number of neighbors. We show how toassess uncertainty in the process and identify the classesof communication topologies that provide greater decision-making accuracy.
Ioannis PoulakakisDepartment of Mechanical EngineeringUniversity of [email protected]
Luca ScardoviInstitute for Automatic Control EngineeringTechnische Universitat [email protected]
Naomi E. LeonardPrinceton [email protected]
MS5
Mixed Mode Oscillations Underly Bursting in Pi-tuitary Cells
Pituitary cells of the anterior pituitary gland secrete hor-mones in response to electrical activity. Several types ofpituitary cells produce short bursts of electrical activitywhich are more effective than single spikes in evoking hor-mone release. These bursts, called pseudo-plateau bursts,are unlike bursts studied mathematically in neurons. Wedescribe an ongoing mathematical study of pseudo-plateaubursting that links this complex behavior to the existenceof canard-induced mixed mode oscillations. With thisknowledge, it is possible to determine the region of pa-rameter space where bursting occurs as well as the numberof spikes per burst. It is also possible to determine the sen-sitivity of the bursting to variations in key ionic currents.
Richard BertramDepartment of MathematicsFlorida State University
130 DS11 Abstracts
MS5
Canard a l’orange: A New Recipe for MultipleTime Scales
We present a fresh look at phenomena associated with mul-tiple time scale dynamics. In particular, we have a twofoldlook at the extreme changes of curvature that give rise tocanards orbits. First, we pinch away regions of fast dynam-ics, leaving a system that switches between slow dynamicsand slides in the pinched region between. This reveals alink between singular perturbation theory, Filippov’s dif-ferential inclusions, and nonstandard analysis. Second, wepresent a criterion to establish whether the conditions forcanards exist; namely, based on inflection curves, we derivean upper bound in the time scale ratio for the occurrenceof canard explosions.
Mathieu DesrochesUniversity of BristolEngineering [email protected]
Mike R. JeffreyUniversity of [email protected]
MS5
Canards and Bifurcation Delays of Spatially Ho-mogeneous and Inhomogeneous Types in Reaction-diffusion Equations
In ODEs of singular perturbation type, the dynamics of so-lutions near saddle-node bifurcations of equilibria are rich.Canard solutions can arise, which, after spending time nearan attracting equilibrium, stay near a repelling branch ofequilibria for long intervals of time before finally return-ing to a neighborhood of the attracting equilibrium (or ofanother attracting state). As a result, canard solutions ex-hibit bifurcation delay. Here, we analyze some linear andnonlinear reaction-diffusion equations of singular perturba-tion type, showing that solutions of these systems also ex-hibit bifurcation delay and are, hence, canards. Moreover,it is shown for both the linear and the nonlinear equationsthat the exit time may be either spatially homogeneous orspatially inhomogeneous, depending on the magnitude ofthe diffusivity.
Tasso J. KaperBoston UniversityDepartment of [email protected]
Peter De MaesschalckHasselt [email protected]
Nikola PopovicUniversity of [email protected]
MS5
Exploring Torus Canards in a Simple NeuronModel
Neurons can exhibit a variety of dynamical states, includ-ing rapid spiking and bursting. We describe these two
states — and their transitions — in a reduced mathemat-ical model of a cerebellar Purkinje cell. We find at thetransition a canard phenomenon that follows temporarilya branch of repelling limit cycles. To explore these dy-namics, we propose a more abstract mathematical modelwhich captures some fundamental aspects of the canardphenomenon.
Mark KramerDepartment of Mathematics and StatisticsBoston [email protected]
MS6
Spread of Avian Influenza in Networks of WildBird Migratory Pathways
Virulent outbreaks of highly pathogenic avian influenza(HPAI) since 2005 have raised the question about the rolesof migratory and wild birds in the transmission of HPAI.Despite increased monitoring, the role of wild waterfowlas the primary source of the highly pathogenic H5N1 hasnot been clearly established. Understanding the entan-gled dynamics of migration and the disease dynamics iskey to prevention and control measures for humans, migra-tory birds and poultry. Migratory routes of various speciescan overlap or cross at certain stopover locations, gener-ating complicated network topology and facilitates diseasespread from one network to others. This can render someintervention measures targeted at reducing disease spreadalong one particular migratory path ineffective. In thistalk we discuss the formulation of a mathematical model ofconnected migratory pathways and analyze how the con-nection between the pathways affects the disease spreadpatterns and effectiveness of potential control strategies.
Lydia BourouibaDepartment of Mathematics #2-348Massachusetts Institute of [email protected]
MS6
Spatiotemporal Distributions of Migratory Birds:Patchy Models with Delay
We derive and analyze a mathematical model for the spa-tiotemporal distribution of a migratory bird species. Thebirds have specific sites for breeding and winter feeding,and usually several stopover sites along the migrationroute, and therefore a patch model is the natural choice.However, we also model the journeys of the birds alongthe flyways, and this is achieved using a continuous spacemodel of reaction-advection type. In this way proper ac-count is taken of flight times and in-flight mortalities whichmay vary from sector to sector, and this information is fea-tured in the ordinary differential equations for the popula-tions on the patches through the values of the time delaysand the model coefficients. The seasonality of the phe-nomenon is accommodated by having periodic migrationand birth rates. The central result of the paper is a verygeneral theorem on the threshold dynamics, obtained usingrecent results on discrete monotone dynamical systems, forbirth functions which are subhomogeneous. For such func-tions, depending on the spectral radius of a certain opera-tor, either there is a globally attracting periodic solution,or the bird population becomes extinct. Evaluation of thespectral radius is difficult, so we also present, for the par-ticular case of just one stopover site on the migration route,a verifiable sufficient condition for extinction or survival in
DS11 Abstracts 131
the form of an attractive periodic solution. This thresholdis illustrated numerically using data from the U.S. Geo-logical Survey on the bar-headed goose and its migrationto India from its main breeding sites around Lake Qinghaiand Mongolia.
Rongsong LiuDeaprtments of Mathematics and EcologyUniversity of [email protected]
MS6
Impact of Heterogeneity on the Dynamics of SEIREpidemic Models
An SEIR epidemic model with an arbitrary distributed ex-posed stage is revisited to study the impact of heterogene-ity on the spread of infectious diseases. The heterogeneitymay come from the disease stages, spatial positions, and in-dividuals’ age or behaviour, resulting in multi-stage, multi-patch, and multi-group models, respectively. For eachmodel, the basic reproduction number R0 is derived andshown to be a sharp threshold: if R0 ≤ 1, the disease-freeequilibrium is globally asymptotically stable and the dis-ease dies out from all stages, patches, or groups; if R0 > 1,the disease persists in all stages, patches, or groups, andthe endemic equilibrium is globally asymptotically stable.
Zhisheng ShuaiDepartment of Mathematics and StatisticsUniversity of [email protected]
MS6
Interactions Among Virulence, Coinfection andDrug Resistance in a Complex Life-cycle Parasite
Motivated by recent empirical studies on Schistosoma man-soni, we use a mathematical model, which consists of ordi-nary differential and integral equations, to investigate theimpacts of drug treatment of the definitive human hostand co-infection of the intermediate snail host by multiplestrains of parasites on the evolution of parasites. Throughthe examination of evolutionarily stable strategies (ESS)of parasites, our study suggests that higher levels of drugtreatment rates (which usually tend to promote monomor-phism as the evolutionary endpoint) will favor parasitestrains that have a higher level of drug resistance and alower level of virulence. Our study also shows that whileco-infection of intermediate hosts does not affect the levelsof drug resistance or virulence of parasites at ESS points, ittends to destabilize ESS points and hence promote dimor-phism or even polymorphism as the evolutionary endpoint.
Dashun XuSouthern Illinois [email protected]
MS7
Stability of Transition Front Solutions in Cahn-Hilliard Systems
We consider the asymptotic behavior of perturbations oftransition wave solutions arising in Cahn–Hilliard systemson R. Such equations arise naturally in the study of phaseseparation, and systems describe cases in which three ormore phases are possible. When a Cahn–Hilliard system is
linearized about a transition wave solution, the linearizedoperator has an eigenvalue at 0 (due to shift invariance),which is not separated from essential spectrum. In manycases, it’s possible to verify that the remaining spectrumlies on the negative real axis, so that stability is entirelydetermined by the nature of this leading eigenvalue. Insuch cases, we identify a stability condition based on anappropriate Evans function, and we verify this conditionunder strong structural conditions on our equations. Moregenerally, we discuss and implement a straightforward nu-merical check of our condition, valid under mild structuralconditions. Finally, we show that this condition is sufficientto establish nonlinear stability.
Peter HowardTexas A&[email protected]
MS7
A Signature-Detecting Evans Function: The KreinMatrix
When considering Hamiltonian eigenvalue problems, it isimportant to locate those purely imaginary eigenvalueswhich have negative Krein signature. These are preciselythe eigenvalues that can lead to spectral instabilities uponperforming some type of parameter continuation in the lin-ear system. The Krein matrix is a real meromorphic matrixof the spectral parameter which is singular precisely at theeigenvalues of the linear system. In this talk I will demon-strate how a careful analysis of the Krein matrix yieldsinformation not only regarding the Krein signature of aneigenvalue, but also information regarding which eigenval-ues are permitted to interact upon performing parametercontinuation. Some open theoretical and practical prob-lems will also be discussed.
Todd KapitulaDepartment of MathematicsCalvin [email protected]
MS7
The Evans Function and the Weyl-TitchmarshFunction
The Evans function is a Wronskian type determinant whichis being used to detect eigenvalues of differential opera-tors that appear when one linearizes partial differentialequations about traveling waves or other special solutions.Recently, some intriguing connections have been studiedbetween the Evans function and other tools in spectraltheory of differential operators. In this talk we describerelations between the Evans function and the classicalWeyl-Titchmarsh function for singular Sturm-Liouville dif-ferential expressions and for matrix Hamiltonian systems.Also, we discuss a related issue of approximating eigenvalueproblems on the whole line by that on finite segments. Fi-nally, for quite general systems, we discuss a formula forthe derivative of the Evans function that uses newly intro-duced modified Jost solutions.
Yuri Latushkin, Alim SukhtayevDepartment of MathematicsUniversity of [email protected], [email protected]
132 DS11 Abstracts
MS7
Asymptotic Linear Stability of Solitary WaterWaves
I will describe a proof (with Shu-Ming Sun) of asymptoticlinear stability of small solitary waves for the 2D Eulerequations for water of finite depth without surface tension.The result involves spatially weighted norms that quantifya unidirectional scattering property, and is related to proofsof nonlinear stability for solitary waves in non-integrablemodel systems such as FPU lattices.
Robert PegoCarnegie Mellon [email protected]
MS8
Simplifying the Dynamical Description of ComplexStochastic Systems
In this talk we present several methodological approachesto developing simplified descriptions of the dynamics ofcomplex systems under the influence of noise. We showthat these methods are particularly effective when the sys-tems satisfy certain multiscale assumptions.
Lee DeVilleUniversity of IllinoisDepartment of [email protected]
MS8
Numerical Methods for Stochastic Bio-chemicalReacting Networks with Multiple Time Scales
Multiscale and stochastic approaches play a crucial rolein faithfully capturing the dynamical features and makinginsightful predictions of cellular reacting systems involv-ing gene expression. Despite their accuracy, the standardstochastic simulation algorithms are necessarily inefficientfor most of the realistic problems with a multiscale naturecharacterized by multiple time scales induced by widelydisparate reactions rates. In this talk, I will discuss somerecent progress on using asymptotic techniques for proba-bility theory to simplify the complex networks and help todesign efficient numerical schemes.
Liu DiMichigan State [email protected]
MS8
Analysis and Numerics for SPDEs with MultipleScales
In this talk we will present analytical and numerical tech-niques for studying stochastic partial differential equationswith multiple scales. After showing a rigorous homog-enization theorem for SPDEs with quadratic nonlineari-ties, we present a numerical method for solving efficientlySPDEs with multiple scales. We then apply these analyt-ical and numerical techniques to several examples, includ-ing the stochastic Burgers and the stochastic Kuramoto-Shivashinsky equation. This is joint work with D. Blomkerand M. Hairer (analysis) and with A. Abdulle (numericalanalysis).
Greg PavliotisImperial College London
MS8
Stochastic Similarity Ultimately Emerges fromSome Stochastic Reaction, Advection, DiffusionEquations
Similarity solutions have an important role in manyapplications—stochastic similarity should also illuminateapplications. Here we explore a class of stochastic reac-tion, advection, diffusion pdes. By transforming to log-time, algebraic decay of diffusion transforms to exponentialattraction of the Gaussian similarity solution. A stochas-tic slow manifold model is then constructed for dynamicsperturbed by small advection, reaction and stochastic forc-ing. The stochastic slow manifold evolution describes theemergent long time dynamics.
Anthony J. RobertsUniversity of [email protected]
MS9
Wave Dynamics in Nonlinear Disordered Media -A Coin with Many Faces
Linear propagation equations for waves in disordered mediaadmit Anderson localization. I will consider cases where alleigenstates of the corresponding wave equations are spa-tially localized, with a finite upper bound on the localiza-tion length. Nonlinear perturbations of the linear equa-tions are often relevant when the wave intensity becomeslarge. Nonlinear terms couple the normal modes (eigen-states) of the linear equations. I will review and presentrecent results and conjectures on the longe time evolutionof nonlinear waves in disordered media. While the com-putational data show destruction of Anderson localizationover many decades in space and time, various edjucatedconjectures are contradicting each other, due to the manyfaces this rich problem has - e.g. integrability vs. noninte-grability, KAM tori vs. deterministic chaos, strong chaosvs. weak chaos, just to name a few.
Sergej FlachMax Planck Institute for the Physics of Complex [email protected]
MS9
Emergence of Generalized Gibbs Distribution inQuantum FPU Problem
We investigate dynamics of quantum mechanical Fermi-Pasta-Ulam model below stochasticity threshold. Quan-tum fluctuations lead to damping of FPU oscillations andrelaxation of the system to a quasisteady state well de-scribed by a generalized Gibbs ensemble with individual-ized temperatures for each momentum mode that are veryweakly mixing in time. This ensemble gives accurate de-scriptions of generic instantaneous correlation functions.We conjecture that GGE generically appears as a prether-malized state in weakly interacting non-integrable systems.
Rafael HipolitoCollege of Staten Island and the Graduate Center [email protected]
DS11 Abstracts 133
MS9
Scaling of Energy Spreading in Strongly NonlinearDisordered Lattices
To characterize a destruction of Anderson localization bynonlinearity, we study the spreading behavior of initiallylocalized states in disordered, strongly nonlinear lattices.Due to chaotic nonlinear interaction of localized linearor nonlinear modes, energy spreads nearly subdiffusively.Based on a phenomenological description by virtue of anonlinear diffusion equation we establish a one-parameterscaling relation between the velocity of spreading and thedensity, which is confirmed numerically. From this scalingit follows that for very low densities the spreading slowsdown compared to the pure power law.
Mario MulanskyDepartment of PhysicsUniversity of Potsdam, [email protected]
MS9
Scaling Properties of Weak Chaos in Nonlinear Dis-ordered Lattices
The Discrete Nonlinear Schroedinger Equation with a ran-dom potential in one dimension is studied as a dynamicalsystem. It is characterized by the length, the strength ofthe random potential and by the field density that deter-mines the effect of nonlinearity. The probability of thesystem to be regular is established numerically and foundto be a scaling function. This property is used to calculatethe asymptotic properties of the system in regimes beyondour computational power.
Arkady PikovskyDepartment of PhysicsUniversity of Potsdam, [email protected]
Shmuel FishmanDepartment of PhysicsTechnion, Haifa, [email protected]
MS10
Collective Enhancement of Temporal Precision inNetworks of Noisy Oscillators
We propose a theoretical framework to examine the effectsof interaction among noisy oscillators on the temporal pre-cision of cycle-to-cycle periods. Our framework is based ona phase model and can deal with arbitrarily directed andweighted networks. We find that the standard deviation ofcycle-to-cycle periods scales with network size N , given as1/
√N , but only up to a certain cutoff size. A biological
interpretation of this cutoff size is discussed.
Hiroshi KoriDivision of Advanced SciencesOchanomizu [email protected]
Yoji KawamuraThe Earth Simulator CenterJapan Agency for Marine-Earth Science and [email protected]
Naoki Masuda
The University of TokyoGraduate School of Information Science and [email protected]
MS10
Collective Phase Response of MacroscopicRhythms in Coupled Oscillator Ensembles
Macroscopic rhythms in nature often arise from synchro-nized ensembles of microscopic oscillators. We developmacroscopic phase description for globally coupled oscilla-tors. Collective phase response of macroscopic rhythms toperturbations is derived from microscopic phase sensitivityof individual oscillators. Based on this framework, macro-scopic synchronization between oscillator ensembles due tomutual interaction is analyzed. We demonstrate that theoscillator ensembles can exhibit anti-phase synchronizationeven if microscopic interaction between individual oscilla-tors is attractive, and vice versa.
Hiroya NakaoDepartment of PhysicsKyoto [email protected]
Yoji KawamuraThe Earth Simulator CenterJapan Agency for Marine-Earth Science and [email protected]
MS10
Complex Dynamics of Oscillator Ensembles afterBreakup of Synchrony
The talk starts with an overview of the topic of minisympo-sium and continues by the analysis of the collective dynam-ics in an ensemble of nonlinearly coupled Stuart-Landauoscillators. Synchronized for weak coupling, the ensembleexhibits various regimes of partial synchrony with increaseof coupling parameters. In particular, we report a novelquasiperiodic regime which appeares after destruction ofsynchrony via Hopf bifurcation. We also illustrate thisregime by numerical study of globally coupled Hindmarsh-Rose neurons.
Michael RosenblumPotsdam UniversityDepartment of Physics and [email protected]
MS10
Non-universal Results in Noise-induced CommonFiring in Active Rotators
We study a system of coupled active-rotators near the ex-citable regime. It enters a phase of synchronous firing asthe diversity (dispersion of the distribution of natural fre-quencies) increases. The transition is found generically forany distribution with well-defined moments but, singularly,it does not appear for the Lorentzian distribution (widelyused in this context for its analytical properties). Thiswarns about the use of Lorentzian-type distributions tounderstand the generic properties of coupled oscillators.
Raul ToralUniversitat de les Illes [email protected]
134 DS11 Abstracts
Luis F. Lafuerza, Pere ColetIFISC, CSIC-UIBPalma de Mallorca, [email protected], [email protected]
MS11
Darboux Integrability–A Historical Survey
I shall begin this talk a brief historical account of the clas-sical methods for finding closed- form, general solutions topartial differential equations. Recent generalizations of themethod of Darboux and the group-theoretic interpretationof this method will be presented and applications to theconstruction of Backlund tranformations described.
Ian AndersonUtah State UniversityDepartment of Mathematics and [email protected]
MS11
Variational Calculus in Invariant Frames
Variational problems with symmetries can be studied moreefficiently by utilizing bases of non-commutative vectorfields that are properly adapted to the geometry of a prob-lem. We will discuss some of the aspects of performing vari-ational calculus relative to such frames, including deriva-tion of Euler-Lagrange equations and establishing Noethercorrespondence between symmetries and conservation laws.Examples from elasticity will be considered.
Irina KoganNorth Carolina State [email protected]
MS11
Higher-Order Variational Integrators UsingProlongation-Collocation
We propose a novel technique for constructing higher-ordervariational integrators based on the EulerMaclaurin for-mula, and collocation at the nodal points using prolon-gations of the Euler-Lagrange vector field. In contrastto traditional methods for constructing higher-order vari-ational integrators, this yields a numerical solution curvewith more regularity at the nodal points, as well as a moreexplicit relationship between the approximation propertiesof finite-dimensional function space used and the order ofaccuracy of the resulting variational integrator. This es-sentially results in a symplectic two-point Taylor method,which is particularly suitable for applications wherein thesolution and its derivatives at the nodal values need to bedirectly accessible, for example in digital feedback controlof mechanical systems.
Melvin Leok, Tatiana ShingelUniversity of California, San DiegoDepartment of [email protected], [email protected]
MS11
Invariant Variational Problems and Invariant Flows
I will introduce the moving frame approach to the analy-sis of invariant variational problems and the evolution ofdifferential invariants under invariant submanifold flows.Applications will include differential geometric flows, inte-
grable systems, Poisson reduction, and image processing.
Peter OlverUniversity of MinnesotaSchool of [email protected]
MS12
Boundaries of Unsteady Lagrangian CoherentStructures
For steady flows, the boundaries of Lagrangian CoherentStructures are segments of manifolds connected to fixedpoints. In the general unsteady situation, these bound-aries are time-varying manifolds of hyperbolic trajectories.Locating these boundaries, and attempting to meaning-fully quantify fluid flux across them, is difficult since theyare moving with time. This talk uses a newly developedtangential movement theory to locate these boundaries innearly-steady compressible flows.
Sanjeeva BalasuriyaConnecticut CollegeDepartment of [email protected]
MS12
Transport in Time-dependent Dynamical Systems:Finite-time Coherent Sets and Applications toGeophysical Fluid Flow
We study the transport properties of nonautonomouschaotic dynamical systems over a finite-time duration. Weare particularly interested in those regions that remain co-herent and relatively nondispersive over finite periods oftime, despite the chaotic nature of the system. We de-scribe a simple methodology that automatically detectsmaximally coherent sets from singular vectors of a matrixof transitions induced by the dynamics. We illustrate ournew methodology on an idealized stratospheric flow and intwo- and three-dimensional analyses of European Centrefor Medium Range Weather Forecasting ECMWFΛ reanal-ysis data.
Gary FroylandUniversity of New South [email protected]
Naratip SantitissadeekornSchool of Mathematics and StatisticsUniversity of New South [email protected]
Adam MonahanSchool of Earth and Ocean SciencesUniversity of [email protected]
MS12
Lagrangian Coherent Structures: An Overview andRecent Analytic Results
After a survey of Lagrangian Coherent Structures (LCS),we describe a mathematical theory that clarifies the rela-tionship between LCS in moving continua and invariants ofthe Cauchy-Green strain tensor field. Motivated by phys-ical observations of trajectory patterns, we define hyper-bolic LCS as material surfaces that extremize an appro-
DS11 Abstracts 135
priate finite-time normal repulsion or attraction measure.Solving this variational problem leads to computable suffi-cient and necessary criteria for LCS. We also discuss con-strained LCS problems, as well as the robustness of LCSunder perturbations, such as numerical errors or data im-perfection. We finally show applications of the new varia-tional theory to geophysical data sets.
George HallerMcGill UniversityDepartment of Mechanical [email protected]
MS12
Coherent Structures and Transport in TransitorySystems
We consider 2D and 3D transitory systems—those whichare nonautonomous only on a compact interval—andpresent a new method for quantifying transport betweenpast and future coherent structures. Our method applies toexact volume-preserving flows and relies on knowing onlythe actions of orbits heteroclinic to backward and forwardhyperbolic sets. We illustrate our theory with examplesincluding a 2D rotating double gyre and a nonautonomous3D ABC flow.
Brock MosovskyDepartment of Applied MathematicsUniversity of Colorado, [email protected]
James D. MeissUniversity of ColoradoDept of Applied [email protected]
MS13
ECCO – Estimating the Circulation and Climateof the Ocean
ECCO aims at estimating the ocean circulation and cli-mate, over the last decades. The 4DVAR framework con-sists of MITgcm and its adjoint. A multitude of insitu andsatellite observations (O(109)) are assimilated, by virtueof atmospheric forcing and ocean mixing adjustments. Ini-tial conditions play a lesser role than in weather forecast-ing, since forward and adjoint models are integrated overdecades without disruption. We will discuss model erroraccumulation and internal parameter adjustments in thiscontext.
Gael Forget, Patrick [email protected], [email protected]
Carl [email protected]
MS13
Correcting Forcing and Stratification Errors in a
Estuary System Using an Ensemble Kalman Filter
An advanced data assimilation system has been set up forthe Chesapeake Bay using an ensemble Kalman filter. Un-like atmospheric models, errors in forcing in the Bay dom-inate the chaotic grown of initial condition errors. Modelerrors, most importantly over-mixing that leads to reducedstratification, are also important. Experiments show thatthe assimilation improves the state using an ensemble offorcing fields as well as adaptive inflation techniques tocounteract forcing and model errors.
Matthew J. HoffmanJohns Hopkins [email protected]
MS13
Non-Gaussian Ensemble Data Assimilation
Ensemble data assimilation alternately (1) computes anensemble of model forecasts and (2) adjusts the ensem-ble toward observed data to initialize the next forecast.Considering the ensemble to represent a Gaussian distri-bution of model states and assuming Gaussian observa-tion errors yields a reduced-rank approximation to the ex-tended Kalman filter, and to variational data assimilationwith quadratic cost function. Relaxing the Gaussian as-sumption, but retaining a local reduced-rank approxima-tion, allows more general cost functions while maintainingcomputational efficiency.
Brian R. HuntUniversity of [email protected]
MS13
Data Assimilation for Cancer Forecasting
This talk describes some issues and results in applying dataassimilation methodology, used in operational weatherforecasting, to mathematical models of cancer. I will de-scribe some recent proof-of-concept results that suggest thepossibility of making short-term (1-2 month) forecasts ofthe future growth of malignant brain tumors.
Eric J. KostelichArizona State UniversityDepartment of [email protected]
MS14
Wave Propagation in Chains of Beads withHertzian Contacts and the p-Schrodinger Equation
Perturbative methods like modulation equations and lo-cal continuation techniques have been used to describe im-portant classes of waves in nonlinear lattices, like solitons,nonlinear normal modes and breathers. Because such ap-proaches require sufficient smoothness and often concernweakly nonlinear waves, their application to uncompressedgranular chains is delicate due to Hertz’s contact forces.We adapt them to granular chains including Newton’s cra-dle, for which a nonlinear Schrodinger equation with dis-crete p-Laplacian captures many dynamical features.
Guillaume JamesLaboratoire Jean Kuntzmann, Universite de Grenobleand [email protected]
136 DS11 Abstracts
MS14
Granular Chains: The Binary Collision Approxi-mation
We generalize the binary collision approximation (BCA)to granular chains with certain geometries in which morethan two granules participate in any collision event. Thisincludes certain decorated granular chains in which smallgranules rattle repeatedly between larger granules, andsome random configurations. We also generalize the BCAto describe localized excitations in nonlinear chains inwhich the particles exhibit attractive as well as repulsiveinteractions.
Katja LindenbergDepartment of Chemistry and BiochemistryUniversity of California San Diego, [email protected]
Upendra HarbolaUniversity of California San [email protected]
Alexandre RosasUniversidade Federal de [email protected]
A. H. [email protected]
MS14
Tailoring Stress Propagation in Granular Media:Effects of Particle and System Geometry
We investigate effects of particle and system geometry onthe propagation of highly nonlinear solitary waves in gran-ular media. For the particle geometry effect, we study 1Dchains composed of ellipsoidal or cylindrical beads. Weshow that the dynamic behavior of the systems dependson particle shape and angle of orientation between parti-cles. For the system geometry effect, we study Y-shapedsystems composed of chains of identical spheres and reportthe dependence on the branch angles of the wave’s proper-ties in two branches.
Duc NgoGraduate Aerospace LaboratoriesCalifornia Institute of [email protected]
Chiara DaraioAeronautics and Applied PhysicsCalifornia Institute of [email protected]
MS14
Nonlinear Resonance Phenomena in GranularDimers with no Pre-Compression
We consider non-compressed granular, dimer chains con-sisting of pairs of heavy and light beads assuming perfectlyelastic Hertzian interaction between beads. A new class ofsolitary waves, satisfying special symmetry conditions, wasdiscovered for these systems. We show that these solitarywaves arise from an infinity of nonlinear resonances in thedimer. Also, we discuss an alternative resonance mecha-nism that leads to the opposite effect, that is, very efficient
shock attenuation in the dimer chain.
Alexander F. VakakisUniv of Illinois @ Urbana-ChampaignDept of Mech/Indust [email protected]
Yuli StarosvetskyUniversity of Illinois at Urbana Champaign1416 Mechanical Engineering [email protected]
K. R. JayaprakashUniversity of Illinois at Urbana - [email protected]
MS15
Random Graphs and Sleep-wake Dynamics
Sleep and wake states are each maintained by activity in acorresponding neuronal network, with mutually inhibitoryconnections between the networks. In infants, the dura-tions of both states are exponentially distributed, but thewake states of adults have a heavy-tailed distribution. Isit the altered network architecture or a change in neuronaldynamics that drives the transformed wake distribution?We use random graph theory to explore this issue and themechanisms of transition between states.
Janet BestThe Ohio State UniversityDepartment of [email protected]
Deena Schmidt, Boris PittelThe Ohio State [email protected], [email protected]
Mark BlumbergUniversity of IowaDepartment of [email protected]
MS15
Neural Networks Computing Relaxations of HardCombinatorial Problems
We present new models of emergent (global) computationin neural sensor networks. These models process input bycomparing a new signal measurement to the signal historystatistics stored in pair-wise synaptic couplings. We alsoexplain the relationship between these models and recentspectral relaxation techniques in computer vision and op-timization. (Joint work with Kilian Koepsell).
Christopher HillarMathematical Sciences Research [email protected]
MS15
Connectivity vs. Dynamics in a Simple Model ofNeuronal Networks
For certain neuronal networks the ODE dynamics can berigorously reduced to a simple discrete-time model N witha finite state space. Probabilistic methods reveal how typ-ical dynamics of N changes with the average in- or out-degree of the connectivity digraph D. Two sharp phase
DS11 Abstracts 137
transitions were found. For certain types of connectivi-ties D we derived optimal bounds for the possible lengthsof the attractors and transients.
Winfried JustDepartment of MathematicsOhio [email protected]
David H. TermanThe Ohio State UniversityDepartment of [email protected]
Sungwoo AhnDepartment of Mathematical SciencesIndiana University Purdue University [email protected]
MS15
Network Dynamics on Random Graphs
A fundamental question regarding neural systems is the ex-tent to which network architecture may contribute to thedynamics occurring on the network. We explore this is-sue by investigating two different stochastic processes ondifferent graph structures, asking how graph structure isreflected in the dynamics of the process. Our findings sug-gest that memoryless processes are more likely to reflectthe degree distribution, whereas processes with memorycan robustly produce heavy-tailed distributions regardlessof degree distribution.
Deena SchmidtThe Ohio State [email protected]
Janet BestThe Ohio State UniversityDepartment of [email protected]
Boris PittelThe Ohio State [email protected]
Mark BlumbergUniversity of IowaDepartment of [email protected]
MS16
Influence of Sensory Feedback on Central PatternGeneration During Stepping Dynamics Near AnOscillatory Domain
Recent experiments have supplied key data on the im-pact afferent excitation has on the activity of the levator-depressor motor system in the stick insect. The main find-ing was that local sensory feedback can completely overruleinter-leg neuronal influences on the level of this distal legjoint. Here, we introduce a neuronal network model of thismotor system and use it to elucidate the mechanisms thatunderlie the neuronal activity seen in the experiments.
Silvia Gruhn, Tibor TothBiocentreUniversity of Cologne
[email protected], [email protected]
MS16
Phase Resetting Properties of Half-Center Oscilla-tors
Half-center oscillators (HCOs) are the fundamental units ofmany pattern generating neuronal networks, including thecircuit underlying locomotion in crayfish. HCOs are com-posed of two reciprocally inhibitory cells that fire in anti-phase. The anti-phase activity can be generated throughtwo mechanisms: escape or release. We show that thesetwo mechanisms give rise to very different phase resettingproperties of HCOs and therefore they can lead to distinctphase-locking dynamics in networks of HCOs.
Tim LewisUniversity of Californiaat [email protected]
Jiawei ZhangUniversity of California, [email protected]
MS16
Pattern-generating Neurons and Pattern-generating Circuits: Phenomena, Signficance, andProblems for Analysis
Nervous systems have encoded in their structures the in-formation required to drive complex natural behaviors, butthe forms this information takes are not obvious and theirdynamics are not well understood. I will present examplesof pattern-generation by single neurons, by local neuralcircuits, and by distributed systems of these local circuits.As the complexity of a system under study increases, ourability to analyze its dynamics rigorously using physicallaws erodes. This opens the field to new mathematical ap-proaches to analysis of these pattern-generating systems,and possibilities for finding new rules of these systems or-ganization.
Brian MulloneyUniversity of California [email protected]
MS16
CPGs and Stability of Locomotion: How NeuralFeedback Enhances Cockroach Running
We have developed an integrated model for insect locomo-tion that includes a central pattern generator, nonlinearmuscles, hexapedal geometry and a representative proprio-ceptive sensory pathway. We employ phase reduction andaveraging theory to reduce complexity, arising from thenumber of neurons, muscles, joints and legs. The reducedorder model allows for analysis of aspects of cockroach lo-comotion such as maneuverability, reflexive feedback, andstability against perturbations.
Joshua ProctorPrinceton [email protected]
Philip HolmesPrinceton UniversityProgram in Applied and Computaional Mathematics &
138 DS11 Abstracts
MS17
Periodic Motions and their Classical Invariants inQuantum Chaos
Poincare unveiled the existence of chaos in dynamical sys-tems, and demonstrated the importance of periodic orbits,and its homoclinic and heteroclinic connections, in the hi-erarchical organization of phase-space. Later Heller pub-lished his seminal work on scar theory showing the impor-tance of POs in quantum dynamics. Using a novel tech-nique to construct scarred wavefunctions, we show thatthe information concerning the associated invariant (ho-moclinic and heteroclinic motions and Lazutkin angle) isalso contained in the system quantum mechanics.
Florentino BorondoUniversidad Autonoma de [email protected]
MS17
How Well Can One Resolve the State Space of aChaotic Flow?
All physical systems are affected by some noise that limitsthe resolution that can be attained in partitioning theirstate space. For chaotic, locally hyperbolic flows, thisresolution depends on the interplay of the local stretch-ing/contraction and the smearing due to noise. Our goal isto determine the ‘finest attainable’ partition for a given hy-perbolic dynamical system and a given weak additive whitenoise. That is achieved by computing the local eigenfunc-tions of the Fokker-Planck evolution operator in linearizedneighborhoods of the periodic orbits of the correspondingdeterministic system, and using overlaps of their widths asthe criterion for an optimal partition. The Fokker-Planckevolution is then represented by a finite transition graph,whose spectral determinant yields time averages of dynam-ical observables. The method applies in principle to bothcontinuous- and discrete-time dynamical systems. Numer-ical tests of such optimal partitions on unimodal maps sup-port our hypothesis.
Predrag Cvitanovic, Domenico LippolisCenter for Nonlinear ScienceGeorgia Institute of [email protected], [email protected]
MS17
Periodic Orbits and Transport in Mixed PhaseSpaces
Though the transport properties of chaotic systems arecomputable from periodic orbits, in practice, such compu-tations are easiest to realize in sufficiently hyperbolic sys-tems dominated by short orbits. Phase spaces exhibiting amixture of chaos and regularity, however, present a greaterchallenge, owing to the richer topological dynamics in thevicinity of stable islands and the importance of longer or-bits. We demonstrate how, using a sufficiently accuratesymbolic dynamics, periodic orbit techniques can computeclassical decay rates even in a strongly mixed phase space.
Kevin A. MitchellUniv of California, MercedSchool of Natural Sciences
MS17
Bunching of Periodic Orbits and Universality inQuantum Chaos
Long periodic orbits of hyperbolic dynamics do not ex-ist as independent individuals but rather come in closelypacked bunches. Under weak resolution a bunch looks likea single orbit in configuration space, but close inspectionreveals topological orbit-to-orbit differences. The construc-tion principle of bunches involves close self-”encounters”of an orbit wherein two or more stretches stay close. Theorbit-to-orbit action differences ΔS within a bunch can bearbitrarily small. Bunches with ΔS of the order of Planck’sconstant have constructively interfering Feynman ampli-tudes for quantum observables. This constructive interfer-ence has profound implications for the quantum proper-ties of classically chaotic systems. In particular it deter-mines the statistics of the energy levels of chaotic systemsand explains why the correlation functions describing thesestatistics have a universal form. Closely related interfer-ence mechanisms between open trajectories determine theconductance and other transport properties of chaotic cav-ities. In my talk I will give an overview over recent researchinto these phenomena.
Alexander AltlandUniversity of [email protected]
Petr Braun, Fritz HaakeUniversitaet [email protected], [email protected]
Stefan HeuslerUniversitaet [email protected]
Sebastian MuellerUniversity of BristolSchool of [email protected]
MS18
Pandemic Influenza Vaccination Timing in a Pop-ulation Dynamical Model
We present a compartmental epidemic model, extended tocapture age structure and transmission network dynam-ics, representing the Greater Vancouver Regional District(population 2 million). Using our model we evaluate theefficacy of pH1N1-influenza vaccination campaigns initi-ated between mid-July/late-November 2009 in terms ofinfections and deaths averted. We consider three vaccine-distribution strategies differing in age-specific coverage andshow that having a good estimate of epidemic peak tim-ing is critical when making policy decisions on vaccinationstrategies.
Jessica M. ConwayUniversity of British ColumbiaDepartment of [email protected]
Ashleigh TuiteDalla Lana School of Public HealthUniversity of Toronto
DS11 Abstracts 139
Rafael MezaUBC Centre for Disease ControlDivision of Mathematical [email protected]
Babak PourbohloulUniversity of British [email protected]
MS18
Stochastic Effects in Infection Dynamics: Simula-tions and Analytical Models
In this talk, we will discuss the mechanisms that gen-erate oscillations in the incidence of childhood infectiousdiseases. We will show that, first, demographic stochas-ticity can generate coherent fluctuations which behave assustained oscillations and, second, the power spectrumof these fluctuations can be calculated analytically usinga van Kampen’s expansion. The combined analysis ofstochastic simulations and data records for measles andwhooping cough for different cities in England, Wales andCanada shows that in systems whose sizes represent realpopulations the role of stochastic effects becomes funda-mental for the interpretation of historical data.
Ganna RozhnovaUniversity of Lisbon, PortugalUniversity of Manchester, UKa [email protected]
Ana NunesUniversity of Lisbon, [email protected]
MS18
Genetic Control of Vector-borne Diseases: Arti-ficial Selection and Heterogeneity of the ImmuneResponse in Mosquitoes
Abstract not available at time of publication.
Claudio StruchinerOswaldo Cruz FoundationProgram for Scientific [email protected]
MS19
Asymptotic Behavior of Stochastically BlinkingSystems
Dynamical systems that are externally driven by stochas-tic processes are good models for many physical, biologicaland engineering systems. The most obvious examples areobtained by the presence of noise, but in many other cir-cumstances, such as e.g. in dynamical networks with ran-domly present links such models are also pertinent. Thereare two time scales present in such randomly switching(blinking) networks, namely the time scale of the individualdynamical system itself and the time scale of the stochas-tic (blinking) process. In this work, we suppose that thestochastic process is much faster than the dynamical sys-tem. We show that with high probability, the solution ofthe stochastic system follows the solution of the averagedsystem with a certain precision for a certain finite lengthof time, if it starts from the same initial condition. As a
perturbation result this is well known. Here, we go muchfarther by giving explicit bounds that relate the probabil-ity, the precision and the length of the time interval to eachother. A result that could not be obtained from the pertur-bation approach is the presence of a soft upper bound onthe length of the time interval, beyond which the solutionof the blinking system can only follow the solution of theaveraged system with good precision for unreasonably faststochastic driving. We also discuss the asymptotic proper-ties of the solutions of the blinking system as time goes toinfinity. The question we address is whether and how thesolutions of the blinking system converge to an attractorof the averaged system.
Martin HaslerSwiss Federal Institute of Technology [email protected]
Vladimir BelykhUniversity of Nizhny [email protected]
Igor BelykhDepartment of Mathematics and StatisticsGeorgia State [email protected]
MS19
The Climate System as a Network of Networks
We introduce a novel graph-theoretical framework forstudying the interaction structure between sub-networksembedded within a complex network of networks. This al-lows us to quantify the structural role of single vertices orwhole sub-networks with respect to the interaction of a pairof subnetworks on local, mesoscopic, and global topologicalscales. Climate networks have recently been shown to be apowerful tool for the analysis of climatological data. Herewe use the concept of network of networks by introducingclimate subnetworks representing different heights in theatmosphere. Parameters of this network of networks, ascross-betweenness, uncover relations to global circulationpatterns in oceans and atmosphere. The global scale viewon climate networks offers promising new perspectives fordetecting dynamical structures based on nonlinear physicalprocesses in the climate system.
Juergen KurthsPotsdam Institute for Climate Impact ResearchHumboldt University Berlin, [email protected]
J. Dongeshs Potsdam Institute for Climate Impact ResearchHumboldt University Berlin, [email protected]
N. Marwan, Y. ZouPotsdam Institute for Climate Impact ResearchHumboldt University Berlin, [email protected], [email protected]
MS19
On Synchronization Over Numerosity-constrainedNetworks with Application to Animal Grouping
Collective behavior of animal groups, such as schools of fishand flocks of birds, is characterized by coordinated maneu-
140 DS11 Abstracts
vers of individuals with matched velocities. The mechan-ics of coordination in animal groups can be assimilated todistributed averaging over networks of coupled dynamicalsystems. The topology of the underlying network describesthe information flow among the agents and thus dictatestheir ability to synchronize. Information flow among groupmates is generally affected by the so-called numerosity thatquantifies a critical limit to the species perception of nat-ural numbers. Groups with cardinality less than the nu-merosity are perceived by an individual as a specific col-lection, while groups of more than this limit are perceivedonly as many. In this paper, we imbed the biologically-observed perceptual phenomenon of numerosity in synchro-nization problems towards establishing a first analyticalunderstanding of the impact of psychological factors oncollective behavior of animal groups. More specifically, weconsider consensus/synchronization of discrete maps thatare coupled via a stochastic network in which every dy-namical system receives information from a fixed numberof agents that are randomly selected at each time step. Forthe consensus problem, we establish necessary and suffi-cient conditions for stochastic consentability based on thenetwork size, the numerosity, and the coupling strength.In addition, we present a master stability function that al-lows for directly assessing the synchronization of the cou-pled dynamical systems in terms of the spectral propertiesof the numerosity-constrained network and the individualdynamics.
Maurizio PorfiriDept. of Mechanical, Aerospace and ManufacturingEngineeringPolytechnic [email protected]
MS19
Intermittent Synchronization in Adaptive Net-works of Coupled Oscillators
Networks of Kuramoto phase oscillators with dynamicallyadapting coupling strengths are studied in the case wherethere is hysteresis in the transition to synchronism (caused,for example, by finite oscillator response times or slow os-cillator frequency adaptation). For a class of local adap-tive rules, the oscillators display “intermittent synchroniza-tion’, in which the oscillators periodically synchronize anddesynchronize on a slow time scale. The conditions forintermittent synchronization are discussed and illustratedby examples. The robustness of this phenomenon to noise,network structure, and finite size effects is studied.
Juan G. RestrepoDepartment of Applied MathematicsUniversity of Colorado at [email protected]
Dane TaylorDept. Applied MathUniversity of [email protected]
Per Sebastian SkardalDepartment of Applied MathematicsUniversity of Colorado at [email protected]
MS20
Microfluidic Rheology and Dynamical Heterogene-
ity of Soft Colloids above and below Jamming
The rheology near jamming of a suspension of soft colloidalspheres is studied using a custom microfluidic rheometerthat provides stress versus strain rate over many decades.We find non-Newtonian behavior below the jamming con-centration and yield stress behavior above it. The datamay be collapsed onto two branches with critical scalingexponents that agree with expectations based on Hertziancontacts and viscous drag. The heterogeneity size is alsoobserved to diverge as power laws in distance to jamming.These results support the conclusion that jamming is sim-ilar to a critical phase transition, but with interaction-dependent exponents.
Douglas DurianDepartment of PhysicsUniversity of [email protected]
Kerstin Nordstrom, Emilie VerneuilUniversity of [email protected]¿, [email protected]
Jerry P. GollubHaverford CollegeDepartment of [email protected]
MS20
Avalanches and Diffusion in Model Bubble RaftsNear Jamming
Energy dissipation distributions and particle displacementstatistics are studied in the mean field version of Durian’sbubble model. A two dimensional (2D) bi-disperse mix-ture is simulated at various strain rates, γ, and packingratios, φ, above the close packing limit, φc. Above φc, atsufficiently low γ, the system responds with a power lawdistribution of energy dissipation. As one increases γ atfixed φ, the intermittent behavior vanishes. Displacementdistributions are non-Fickian at short times but cross to aFickian regime at a universal strain, Δγ∗, independent ofγ and φ. Surprisingly, despite the profound differences inshort-time dynamics, at intermediate Δγ, the systems ex-hibit qualitatively similar spatial patterns of deformation,with lines of slip extending across large fractions of thesimulation cell.
Craig MaloneyCivil & Environmental EngineeringCarnegy Mellon University, [email protected]
MS20
Asymmetries and Velocity Correlations in ShearingMedia
A model of soft frictionless disks in two dimensions at zerotemperature is simulated with a shearing dynamics aroundthe jamming density. First focusing on single particle prop-erties we find that both the particle velocities and the inter-particle forces have interesting features at jamming. Turn-ing to velocity correlations we examine a mixed correlationfunction that happens to decay exponentially to an excel-lent approximation. From the exponential decay we extracta correlation length that shows strong evidence of critical
DS11 Abstracts 141
scaling.
Peter OlssonDepartment of PhysicsUme{aa} University, [email protected]
MS20
Non-Newtonian Rheology of Sheared Soft SphereSystems near the Jamming Point: An Introduction
In this talk I will both give an introduction to the ma-jor theme of the symposium and present our recent theoryfor the rheology of sheared soft spheres near the jammingpoint. I first review some essentials of the jamming the-ory for static packings of soft (compressible) spheres. Bybuilding on what we now understand about the anomalous”floppy” modes near jamming, I then develop a theory forthe rheology of sheared soft sphere systems.
Wim van SaarloosFOM FoundationLeiden [email protected]
MS21
A Game-theoretic Approach to the Vertical Distri-bution of Phytoplankton
We show how both extrinsic and intrinsic factors interactto determine spatial patterns in phytoplankton commu-nities. Determinants of the spatial (vertical) distributionof phytoplankton remain under-investigated and untested.One of the leading hypotheses to explain phytoplanktonvertical distribution patterns is that competition for essen-tial resources, nutrients and light, in opposing gradientsdetermines vertical distribution. We used a combinationof mathematical modeling, experiments in plankton tow-ers, and surveys across major environmental gradients tostudy what determines the vertical distribution of phyto-plankton, focusing on competition for nutrients and light.
Jarad MellardUniversity of [email protected]
MS21
Bistability in Vertical Distributions of Phytoplank-ton in a Stratified Water Column
Light and nutrients form opposing vertical gradients. Phy-toplankton grow along the resource gradients, typicallyshowing a unimodal vertical distribution. Recent numeri-cal studies suggest bistability in steady state when a wa-ter column is composed of a well-mixed surface layer anda poorly-mixed deep layer. I discuss mechanisms of thebistability and structure of the bifurcation set.
Kohei YoshiyamaThe University of Tokyo, [email protected]
MS21
Emergence and Annihilation of Localized Struc-
tures in a Phytoplankton-nutrient System
We consider a model describing marine phytoplankton, thegrowth of which is co-limited by both light and nutrient.Our goal is to investigate analytically the weakly nonlineardynamics of deep chlorophyll maxima (DCM) beyond thelinear regime. Exploiting the model’s natural singularlyperturbed nature, we derive an explicit reduced model ofasymptotically high dimension fully capturing these dy-namics. Using it, we find that bifurcating DCM patternsare soon annihilated in a saddle-node bifurcation.
Antonios Zagaris
Universiteit Twente (NL)CWI, Amsterdam (NL)[email protected]
MS21
A Weakly Nonlinear Model for Phytoplankton Pat-tern Formation in Estuaries
An idealised model is analysed to gain fundamental under-standing about the dynamics of phytoplankton blooms inwell-mixed, suspended sediment dominated estuaries. Themodel describes the behaviour of currents, suspended sed-iments, nutrients and phytoplankton in a channel. Theinitial growth of phytoplankton and its spatial distributionis calculated by solving an eigenvalue problem. It is demon-strated how the onset of blooms in the model depends onphysical and biological processes.
Huib de SwartIMAU, Utrecht UniversityPO Box 80005 Utrecht [email protected]
MS22
Frame Selection in Nonholonomic Mechanics
Appropriate selection of a moving frame can simplify theequations of nonholonomic mechanics by eliminating thenecessity to solve for velocity components not containedwithin the constraint distribution. We discuss the rela-tion of the Hamel equations to the reduced equations oneobtains using a fiber bundle description, and introduce in-termediary forms for the equations of motion. Finally weapply these equations to several physical systems to betterunderstand their benefit.
Jared M. MaruskinSan Jose State [email protected]
MS22
From Brakes-to-Syzygy in the Three-Body Prob-lem
In this joint work with Rick Moeckel and Andrea Venturellian investigation of brake orbits in the 3-body problem arosenaturally in trying to better understand properties of the“syzygy’ cross section, and the resulting symbol (syzygy)sequences. We present progress on several open problems.
Richard MontgomeryDept of MathematicsUniversity of California-Santa [email protected]
142 DS11 Abstracts
MS22
Automatically Generated Variational Integrators
Differential-geometric structures enable differential equa-tions to model special, interesting properties of importantphysical systems. Geometric mechanics is concerned withpenetrating and fundamental advances formulated in termsof the structures from which the differential equations arederived. Upon providing an overview of current trends, Iwill specifically describe advances in the theory of struc-ture preserving integrators, and a software system calledAUDELSI, which converts any ordinary one step methodinto an equal order variational integrator.
George PatrickDept of Math & StatisticsUniversity of [email protected]
MS22
Structure-Preserving Integrators for ChaplyginSystems
When simulating mechanical systems numerically, it maybe desirable to preserve various intrinsic structures. For in-stance, in the absence of velocity constraints, it is desirableto preserve a symplectic form. Many of these structures failto be invariant in systems with velocity constraints. Inte-grators that preserve suitable quantities in the presence ofvelocity constraints will be introduced.
Dmitry ZenkovNorth Carolina State UniversityDepartment of [email protected]
Cameron LynchNorth Carolina State UniversityElectrical and Computer [email protected]
MS23
Fast Computation of Time-Varying Finite TimeLyapunov Exponents
This work investigates a number of efficient methods forcomputing finite time Lyapunov exponent (FTLE) fieldsin unsteady flows. The methods approximate the parti-cle flow map, eliminating redundant particle integration inneighboring flow map calculations. Two classes of flow mapapproximations are investigated based on composition ofintermediate flow maps; unidirectional approximation con-structs a time-T map by composing a number of smallertime-h maps, while bidirectional approximation constructsa flow map by composing both positive and negative-timemaps. An error analysis is presented which shows thatthe unidirectional methods are accurate while the bidirec-tional methods have significant error which is aligned withthe opposite-time coherent structures. This is explainedby the fact that material near the positive-time LCS willattract onto the negative-time LCS near time-dependentsaddle points. The algorithms are implemented and com-pared on three example fluid flows: a double gyre, a lowReynolds number pitching flat plate, and an unsteady ABCflow. The unidirectional methods are both fast and accu-rate, providing orders of magnitude computational savingsover the standard method when computing a sequence of
FTLE fields in time for an unsteady flow.
Steven L. BruntonPrinceton [email protected]
Clarence RowleyPrinceton UniversityDepartment of Mechanical and Aerospace [email protected]
MS23
An Eulerian Approach for Computing the FiniteTime Lyapunov Exponent
In this talk we present an Eulerian method for computingthe finite-time Lyapunov exponent (FTLE). The idea is tocompute the related flow map using the level set methodand the Liouville equation. When determining the flowmap, the algorithm requires the velocity field defined onlyat mesh locations. We also extend the algorithm to com-pute the FTLE on a co-dimension one surface. The methoddoes not require any local coordinate system and is simpleto implement even for evolving manifolds.
Shingyu LeungHong Kong University of Science and [email protected]
MS23
Ridge Surface Methods for the Visualization ofLCS
In visual analysis of flow data, an increasingly popularmethod is the extraction of Lagrangian coherent structures(LCS). For the computation of LCS we follow the definitionof LCS as being ridges of the finite-time Lyapunov expo-nent (FTLE) and explore several existing ridge definitions.We give a comparison of the obtained LCS in terms of ac-curacy and noisiness, and we propose a new ridge definitiontailored to FTLE data. Finally, we investigate FTLE ridgesin scale-space and propose a new optimality criterion.
Ronald PeikertDepartment of Computer ScienceETH [email protected]
MS23
Efficient Computation of Lagrangian CoherentStructures for Interactive Visual Analysis in Com-putational Fluid Dynamics
We will start by discussing the computational challengesassociated with LCS in numerical datasets. We will pro-ceed with a brief overview of the existing algorithms for theefficient extraction of LCS. We will then describe recent ad-vances in the interactive visual exploration of LCS acrossspatial resolutions and present a novel high-performancemethod for the geometric extraction of accurate LCS fromFTLE fields in scale space. Results will be shown in ana-lytical and CFD datasets.
Xavier M. TricochePurdue UniversityWest Lafayette, IN [email protected]
DS11 Abstracts 143
MS24
Effects of Nonlinear Saddles and Centers on DataAssimilation
The main focus of this talk will be the effect of two basicnonlinear phenomena - the shear around a nonlinear centerand the divergence of trajectories near a nonlinear saddlepoint - on data assimilation. The rich nonlinear dynamicalfeatures of Lagrangian particles in a fluid flow allows us tonaturally isolate these features and study their effects. Inparticular, we will discuss how the nonlinearities lead tothe appearance of non-Gaussian distribution functions.
Amit ApteTIFR Centre for Applicable MathematicsBangalore, [email protected]
Christopher JonesUniversity of North Carolina and University of [email protected]
MS24
Forecasting Regime Changes in a Chaotic Toy Cli-mate
A low-dimensional model of natural convection in a ther-mosyphon, analogous to Lorenz’ 1963 system, is comparedto direct numerical flow simulations as a testbed for dataassimilation in the presence of model error. The flow dy-namics of the thermosyphon exhibit distinct behavioralregimes, so we consider the thermosyphon a useful toymodel for climate. The reference ”true” state is repre-sented by a long time direct numerical simulation of theflow; forecasts are made using the low-dimensional modeland synchronized to noisy and limited observations of thetruth. We compare results using four separate data as-similation algorithms, varying analysis windows and leadtimes, and show successful forecasting of regime changesand residency times.
Kameron D. HarrisUniversity of [email protected]
Chris DanforthMathematics and StatisticsUniversity of [email protected]
MS24
Variance Limiting Kalman Filtering: ControllingCovariance Overestimation and Model Error
We consider the problem of overestimation of error covari-ances due to model error in data assimilation problems.Artificial viscosity is often used in numerical weather pre-diction models to ensure numerical stability, at the expenseof poorly representing the conservation laws. If this damp-ing is relaxed the model overestimates forecast error covari-ances. Overestimation typically occurs for small ensem-bles in sparse observational networks, and is exacerbatedif there is model error due to underdamped dynamics. Wepropose an alternative to using underdamped dynamics inensemble Kalman filtering, instead using a weak constraintmethod called a variance limiting Kalman filter to controlthe covariance overestimation. We demonstrate our results
numerically using the Lorenz-96 model.
Lewis Mitchell, Georg GottwaldUniversity of [email protected], [email protected]
Sebastian ReichUniversitat [email protected]
MS24
Lagrangian Data Assimilation for Nonlinear OceanProcess Models
Coherent structures drive important ocean dynamics, butare not easily characterized by traditional data assimila-tion techniques. Such Kalman-based techniques performpoorly on strongly nonlinear systems where underlyingphysics leads to non-Gaussian distributions of state vari-ables or parameters of interest. Sampling-based filteringmethods, however, naturally handle this problem and arepromising tools for using data and models to describe oceanprocesses. We will present challenges and results usingsampling-based methods in the context of ocean processes.
Elaine SpillerMarquette [email protected]
MS25
3D Aspects of Mixing and Transport in TumbledGranular Flow
Tumbled granular flow in a spherical container rotated se-quentially about two axes is a realistic system in which toinvestigate kinematic structures of 3D volume-preservingmaps. The dynamics can be restricted to 2D invariantsurfaces, or be fully-3D, depending on the rates of rota-tion. For the former, KAM-like tubes (barriers to mixing)and manifolds (progenitors of mixing) can be constructedby stacking up their 1D versions from a sequence of invari-ant surfaces. Departures from the “perturbed Hamiltoniansystem” template are observed.
Ivan C. Christov, Richard M Lueptow, Julio M OttinoNorthwestern [email protected],[email protected], [email protected]
Rob SturmanUniversity of [email protected]
Stephen WigginsUniversity of [email protected]
MS25
Formation of Coherent Structures by Fluid Inertiain 3D Laminar Flows
We discuss the formation and interaction of coherent struc-tures that geometrically determine the transport proper-ties of laminar flow. The impact of these structures on3D laminar mixing will be demonstrated numerically andexperimentally. Key result is the role of fluid inertia thatinduces partial disintegration of coherent structures of thenon-inertial limit into chaotic regions and merger of surviv-
144 DS11 Abstracts
ing parts into intricate 3D structures. The response followsa universal scenario and reflects an essentially 3D route tochaotic mixing.
Herman ClercxFluid Dynamics Laboratory, Dept. Applied PhysicsEindhoven University of [email protected]
Michel SpeetjensLaboratory for Energy Technology, Dept. Mech. Eng.Eindhoven University of [email protected]
MS25
Adiabatic Mixing: Improved Invariants and Re-fined Boundaries
We present a quantitative long-term description of resonantmixing in 3-D near-integrable flows. We illustrate thatscattering on resonance and capture into resonance createmixing by causing the jumps of adiabatic invariants. Wecalculate the real width of the mixing domain (includingstreamlines approaching but not crossing the resonance),and show the use of improved adiabatic invariants. We il-lustrate that the resulting mixing can be described in termsof a diffusion-type PDE.
Dmitri VainchteinDept. of Mechanical EngineeringTemple University, [email protected]
Alimu AbuduTemple [email protected]
MS25
Mixing in a Tilted Rotating Tank
An example of periodic shear in a tilted rotating tank ge-ometry is discussed to understand the stirring on an inho-mogeneous fluid stirring by periodic shear. The mechanismfor stirring in a flow exhibiting periodic shear is linear orquadratic stretching of material lines. Since periodic shearflows involve only stretching they are typically not as effi-cient as other mixing process that incorporate folding andtwisting along with exponential stretching of material lines.
Thomas WardDepartment of Mechanical and Aerospace EngineeringNC State Universitytward@ncsu
MS26
Combinatorics of Stable Sets and Learning in Re-current Networks
Networks of neurons in some brain areas are flexible enoughto encode new memories quickly. Using a standard firingrate model of recurrent networks, we develop a theory offlexible memory networks. Our main results characterizenetworks having the maximal number of flexible memorypatterns, given a constraint graph on the networks connec-tivity matrix. Modulo a mild topological condition, wefind a close connection between maximally flexible net-works and rank 1 matrices. The topological condition isH1(X; Z) = 0, where X is the clique complex associated
to the networks constraint graph; this condition is generi-cally satisfied for large random networks that are not overlysparse. This is a joint work with Anda Degeratu and Ca-rina Curto.
Vladimir ItskovDepartment of MathematicsUniversity of Nebraska, [email protected]
MS26
Dynamical Moment Neuronal Network: Model andApproach
I shall present a theoretical framework on spike activitiesof leaky-and-integrate networks by including the first-order(mean firing rate) and the second-order statistics (varianceand correlation), based on a moment neuronal network(MNN) approach. The dynamics and distribution of neu-ral activities are approximated as a Gaussian random field.Using this novel model, I shall introduce analysis of severalinteresting phenomena of MNN and illustrate the compu-tation capability of this model with experimental data.
Wenlian LuSchool of Mathematical SciencesFudan [email protected]
Jianfeng FengCentre for Scientific Computing, Warwick UniversityCoventry CV4 7AL, [email protected]
MS26
Using Feed-forward Maps to Explore the Role ofSynaptic Dynamics in a Reciprocally InhibitoryNetwork
Recent data from our lab shows that inhibitory synapses ina CPG network can show a maximal conductance at a pre-ferred presynaptic frequency. We explore a network of twomodel neurons coupled with synapses that show frequencypreference. As a first approximation, the dynamics of eachneuron can be described by a logistic map with two param-eters, resulting in a bifurcation diagram characterized by aperiod-doubling cascade leading to chaotic dynamics.
Farzan NadimNew Jersey Institute of Technology& Rutgers [email protected]
Myongkeun OhNew Jersey Institute of [email protected]
MS26
Networks of Phase-amplitude Neural Oscillators
If the limit cycle is not strongly attracting, the phase de-scription of a neural oscillator may poorly characterise thebehaviour of the original system. Here we consider, forsome well known neural models, a phase-amplitude frame-work, incorporating the distance from the cycle as well asthe phase along it. We present our results using this frame-work for networks of pulse coupled cells, and for networks
DS11 Abstracts 145
coupled via gap junctions.
Kyle C. Wedgwood, Stephen CoombesUniversity of [email protected],[email protected]
MS27
Nonlinear Stability for a Model of a Source-typeDefect
Analyzing the nonlinear stability of source-type defects inreaction-diffusion equations leads to two complicating fac-tors: a nonlocalized eigenfunction and advection that isdirected outward. In preparation for overcoming these inthe general case, it is demonstrated how to do so in thecase of a model equation using a modification of pointwiseestimates that have been successfully used in the setting ofviscous shocks.
Margaret BeckDepartment of Mathematics and StatisticsBoston [email protected]
Toan NguyenDivision of Applied MathematicsBrown UniversityToan [email protected]
Bjorn SandstedeBrown Universitybjorn [email protected]
Kevin ZumbrunIndiana [email protected]
MS27
Nonlinear Stability of Fronts and Pulses for a Classof Reaction-diffusion Systems that Arise in Chem-ical Reaction Models
Motivated by the model for exothermic-endothermic chem-ical reactions we consider a class of reaction-diffusion sys-tems that have traveling wave solutions that possess un-stable continuous spectrum. We formulate assumptionson the reaction terms and the properties of the travel-ing waves (fronts or pulses) under which the convectivecharacter of the instability of the waves can be proved an-alytically. The proof is based on exponential weights andbootstrapping argument to obtain a-priori estimates for theperturbations to the wave. The results are precise enoughto capture real features of phenomena such as endothermic-exothermic chemical reactions.
Anna GhazaryanDepartment of MathematicsMiami University and University of [email protected]
Yuri LatushkinUniversity of Missouri, [email protected]
Stephen SchecterNorth Carolina State University
Department of [email protected]
MS27
Stability of the Line Soliton of the KP-II Equationin L2(Rx × Ty)
We prove the nonlinear stability of line-solitons to the KP-II equation with respect to periodic transverse perturba-tions. Line soliton solutions are saddle points of the energyfunctional but it is infinitely indefinite. Our idea is to usethe Miura transform and show that stability of line solitonsis equivalent to the stability of the null solution.
Tetsu MizumachiFaculty of MathematicsKyushu University, [email protected]
Nikolay TzvetkovUniversit’e de [email protected]
MS27
Geometric Evolution of Structured Interfaces
A central problem in polymer chemistry is to design ma-terials with novel macroscopic properties by controllingthe spontaneous generation of nanoscaled, phase separatednetworks. A primary mechanism to generate such networksis through the “functionalization’ of hydrophobic polymerchains and nanoparticles by the addition of acid or alka-line terminated side-chains. When mixed with solvent, thecharged end-groups accumulate at the solvent-polymer in-terface where access to the solvent shields their electricfield, lowering the electrostatic energy. This accumulationof charged groups engenders a tremendous growth of sol-vent accessible interface, to levels of 1000 m2/gram, amongthe highest known. The resultant networks, by virtue ofthe tethered charge groups lining the interface, are selec-tively conductive, inhibiting the transport of co-ions whilefacilitating the transport of counter-ions, and have impor-tant applications in efficient energy conversion devices suchas polymer electrolyte membrane fuel cells, dye sensitizedsolar cells, bulk-heterojunction solar cells, and lithium ionbatteries. We present a novel class of energies whose gradi-ent flows generate interface in a controllable manner, driv-ing micron scale mixtures into nanoscaled networks. Wediscuss this in the context of the unfolding of critical pointsof classical second order energies as embedded in a fourthorder variational energy. For certain classes of energieswe will show that the geometric evolution of the interfacescouples to the structure of the interface.
Keith PromislowMichigan State [email protected]
MS28
Optimal Control for Globally Coupled Neural Net-works
We consider the problem of desynchronizing a network ofsychronized, globally (all-to-all) coupled neurons using aninput to a single neuron. This is done by applying thediscrete time dynamic programming method to reducedphase models for neural populations. This technique nu-
146 DS11 Abstracts
merically minimizes a certain cost function over the wholestate space, and is applied to a Kuramoto model and a re-duced phase model for Hodgkin-Huxley neurons with elec-trotonic coupling. We also evaluate the effectiveness ofcontrol inputs obtained by averaging over results obtainedfor different coupling strengths.
Jeff MoehlisDept. of Mechanical EngineeringUniversity of California – Santa [email protected]
MS28
Synchronization Control of Interacting OscillatoryEnsembles by Mixed Nonlinear Delayed Feedback
We discuss a method for the control of synchronization intwo oscillator populations interacting according to a drive-response coupling scheme. The response ensemble of oscil-lators, which gets synchronized because of a strong forc-ing by the intrinsically synchronized driving ensemble, iscontrolled by the mixed nonlinear delayed feedback. Thestimulation signal is constructed from the mixed macro-scopic activities of both ensembles according to the rule ofnonlinear delayed feedback. We show that the suggestedmethod can effectively decouple the interacting ensemblesfrom each other, where the natural desynchronous dynam-ics can be recovered in a demand-controlled way either inthe stimulated ensemble, or in both stimulated and notstimulated populations. We discuss possible therapeuticapplications in the context of the control of abnormal brainsynchrony in loops of affected neuronal populations.
Oleksandr PopovychInstitute of Neuroscience and Medicine -NeuromodulationResearch Center Juelich, [email protected]
Peter A. TassInstitute of Medicine (MEG)Research Centre [email protected]
MS28
Model Based Control of Seizures and Parkinson’sDisease
We seek to fuse computational models of neurons and net-works with measurements to assimilate data and controlpathological neuronal dynamics. This strategy involves theframework from ensemble Kalman filters, with either ionicor reduced models of neuronal dynamics, as well as the dy-namics of the ionic environment the neurons are embeddedwithin. We will show recent findings from data assimilationfrom neuronal networks and efforts of creating a rigorouscontrol strategy to modulate such networks.
Steven J. SchiffPenn State UniversityCenter for Neural [email protected]
MS28
Stimulation and Information in the Peripheral Ner-vous System
Cochlear implants are neural prostheses that provide soundinformation by stimulating the auditory nerve with electri-cal pulse trains. We model the response of the auditorynerve via point process and integrate-and-fire models, andquantify the temporal encoding properties of these mod-els using ideal observer analyses and decoding algorithmsthat predict some features of observed data. Throughout,we emphasize the characteristics of both the auditory nerveand decoding systems that are required to make this con-nection, and comment the implications for optimal stimu-lation patterns.
Eric Shea-BrownDepartment of Applied MathematicsUniversity of [email protected]
MS29
Investigating the Spatiotemporal Dynamics of Pan-demic Influenza in Europe
Despite the rapidity of the 2009 H1N1 pandemic influenzain reaching a large number of countries, its spread wasrather heterogeneous also within single continents. Byusing a model able to capture the structure of complexmodern human societies, the reasons underlying this phe-nomenon are thoroughly investigated and the (remarkable)implications for correctly informing public health decisionmakers are highlighted.
marco AjelliBruno Kessler Foundation,[email protected]
Stefano MerlerBruno Kessler [email protected]
MS29
A Toy Model for Epidemics in Rio de Janeiro: TheImportance of the Network Structure
Epidemics modeling has been particularly growing in thepast years. In epidemics studies, mathematical modeling isused in particular to reach a better understanding of someneglected diseases (dengue, malaria, ...) and of new emerg-ing ones (SARS, influenza A,....) of big agglomerates. Suchstudies offer new challenges both from the modeling pointof view (searching for simple models which capture themain characteristics of the disease spreading), data anal-ysis and mathematical complexity. We are facing oftenwith complex networks especially when modeling the citydynamics. Such networks can be static (in first approx-imation) and homogeneous, static and not homogeneousand/or not static (when taking into account the city struc-ture, micro-climates, people circulation, etc.). The objec-tive being studying epidemics dynamics and being able topredict its spreading.
Stefanella BoattoUniversdade Federal de Rio de Janeiro, [email protected]
Francisco C. SantosDepartment of Computer Sciences
DS11 Abstracts 147
New University of Lisbon, [email protected]
Lucas StolermanDepartment of Applied MathematicsFederal University of Rio de Janeiro, [email protected]
Claudia CodecoFundao Oswaldo Cruz, [email protected]
Renata Stella KhouriDept. of Applied Mathematics, UFRJFederal University of Rio de Janeiro, [email protected]
MS29
Multiscale Networks and the Spatial Spread of In-fectious Diseases
Human mobility and interactions represent key ingredientsin the spreading dynamics of an infectious disease. Theflows of traveling individuals form a network character-ized by complex features, such as strong topological andtraffic heterogeneities, that unfolds at different temporaland spatial scales, from short ranges to the global scale.Computational models can be developed that integrate de-tailed network structures based on demographic and mobil-ity data, in order to simulate the spatial evolution of an epi-demic. Focusing on the 2009 H1N1 influenza pandemic as aparadigmatic example, these approaches allow quantifyingthe effects of travel restrictions in delaying and controllingthe epidemic spread. In addition, simplified model frame-works can be solved providing the assessment of the inter-play between individual mobility and epidemic dynamics,under different conditions of heterogeneities characterizinghuman mobility.
Vittoria ColizzaComputational Epidemiology LabISI Foundation, Torino, [email protected]
MS29
The Role of Immunity and Seasonality in CholeraEpidemics
This is a mathematical model for cholera epidemics whichcomprises seasonality, loss of host immunity and controlmechanisms acting on cholera transmission dynamics. Acollection of the data related to cholera disease allows usto show that outbreaks in endemic areas are subject to aresonant behavior, as the intrinsic oscillation period of thedisease (∼ 1 year) is synchronized with the annual contactrate variation. Moreover, we argue that a finite duration ofhost immunity may be associated to the secondary peaksof incidence observed in some regions (a bimodal pattern).Furthermore, we explore some possible scenarios of con-trol mechanisms applied to stopping or diminishing choleraoutbreaks and analyze their efficiency. Besides mass vac-cination - which may be impracticable - improvement ofwater treatment is the most effective way to prevent anepidemic.
Roberto A. KraenkelInstituto de Fsica [email protected]
Rosangela SanchezPrograma de Pos-Graduao em Biometria - UNESP, [email protected]
Claudia Pio Ferreirarograma de Pos-Graduao em Biometria - UNESP, [email protected]
MS30
Adaptive Networks and the Spontaneous Emer-gence of Modularity and Heterogeneity
Structural (topological) and dynamical (synchronization)features co-evolve in an adaptive network of phase oscilla-tors, as soon as two basic biological principles (Hebbian andHomeostatic plasticity) are taken into account for the selec-tion of the local coupling strength between the networkingunits. Synchronization is enhanced, and the combinationof the two adapting mechanisms leads to the spontaneousemergence of highly modular architectures in connectionwith a power-law scaling for the distribution of the self-adapted weights of interactions.
Stefano BoccalettiCNR-Istituto dei Sistemi [email protected]
MS30
Evolving Dynamical Networks for Synchronization:Analysis and Emergent Properties
The aim of this talk is to discuss how to dynamically evolvenetworks of dynamical agents to enhance their synchroniza-tion performance. A new analytical and computationalframework will be introduced that can be used to opti-mize the network topology to best perform a certain de-sired function. Then, the evolution of motifs and othertopological features as the network structure self-evolve toachieve synchronization will be investigated. New inde-ces to characterize evolving networks will be discussed andused to analyze a case study from biology.
Mario Di BernardoUniversity of BristolDept of Engineering [email protected]
Thomas GorochowskiUniversity of [email protected]
MS30
Creating Delay-tolerant Networked DynamicalSystems via Designing the Network Graphs
Dynamical systems coupled over networks arise in manyapplications including neural networks, tele-operation, co-ordination of unmanned vehicles, and vehicular traffic flow.Often, the information transmission among the systems inthese networks does not occur instantaneously, but afterdelays. This means that each system is aware of onlydelayed states of the remaining systems in the network.In this setting, if all the systems make decisions basedon the available, yet delayed information, then the entirenetworked dynamical systems may become unstable. Thelargest amount of delay that the network can withstand be-fore losing stability is called the delay margin. The delaymargin is a measure of how tolerant the network is to the
148 DS11 Abstracts
presence of delays. In large scale networks, existing stud-ies fall short to characterize the delay margin, mainly dueto the scale of the problem. In this talk, on a benchmarkconsensus dynamics, we will present have the delay mar-gin can be calculated in large scale networks using the newconcept called the Responsible Eigenvalue (RE). The REconcept allows reducing the stability analysis of the net-work to the analysis of one and only one eigenvalue of thegraph Laplacian of the network. That is, RE establishesthe indirect link between stability of networked systemswith delays and the graphs of these networks. With such adramatic reduction in complexity, it then becomes possibleto construct mathematical tools that reveal guidelines asto how to manipulate RE such that the delay margin ofa network can be maximized. These tools also lead to de-sign rules by which the network graph can be reconstructedin a way to maximize the delay margin, and new controldesign strategies with which the members of the networkcan autonomously make decisions in order to maintain thestability of the network dynamics.
Rifat SipahiDepartment of Mechanical and Industrial EngineeringNortheastern [email protected]
Wei QiaoNortheastern [email protected]
MS30
Period Doubling and Macroscopic Chaos in a Time-varying Network of Globally Coupled Phase Oscil-lators
The Kuramoto system has been a very successful modelin demonstrating the emergence of collective rhythm fromcoupled biological and physical networks. Using a recentlydeveloped reduction technique, we were able to exactly an-alyze the macroscopic dynamics for a Kuramoto systemwhich includes distinct interacting subnetworks and time-dependent coupling in the thermodynamic limit. These ex-tensions were motivated by real neurological networks withinteracting subpopulations of neurons and intrinsic timevariations. Despite the simple dynamics of the individualunits, we were able to show that the macroscopic mean-field can behave chaotically. Cascades of periodic doublingbifurcations and crises were identified.
Paul SoGeorge Mason UniversityThe Krasnow [email protected]
MS31
Transport Barrier In The Nontwist Standard Map
Nontwist systems, common in the dynamical descriptionsof fluids and plasmas, possess a shearless invariant curvewith a concomitant transport barrier that eliminates or re-duces chaotic transport, even after its breakdown. To in-vestigate the transport properties of nontwist systems, weanalyze the transport barrier breakdown for the standardnontwist map, a paradigm of such systems. We show thatthe transport dependence on the map parameters can beexplained by a sequence of bifurcations that changes thechaotic orbit stickiness and the associated role played by
the dominant crossing of stable and unstable manifolds.
Ibere L. CaldasInstitute of PhysicsUniversity of Sao [email protected]
Jose D. SzezechUniversity of So [email protected]
Sergio LopesDepartment of PhysicsFederal University of [email protected]
Ricardo L. VianaFederal University of [email protected]
P.J. MorrisonDepartment of PhysicsThe University of Texas at [email protected]
MS31
Interplay of Magnetic Shear and Resonances inMagnetic Fusion Devices
The dual impact of low magnetic shear is shown in a uni-fied way with extension to non-axisymmetric states. Awayfrom resonances, it induces a drastic enhancement of mag-netic confinement that favors robust internal transport bar-riers (ITBs) and turbulence reduction. When low-shearoccurs for values of the winding of the magnetic field linesclose to low-order rationals, the amplitude thresholds of theresonant modes that break internal transport barriers byallowing a radial stochastic transport of the magnetic fieldlines may be quite low. This analysis puts a constraint onthe tolerable mode amplitudes compatible with ITBs andis shown to be consistent with diverse experimental andnumerical signatures of their collapses.
Marie-Christine FirpoLaboratoire de Physique des PlasmasEcole Polytechnique, Palaiseau Cedex, [email protected]
Dana ConstantinescuDept of Applied Mathematics, AssociationEuratom-MECIUniversity of Craiova, Craiova 200585, [email protected]
MS31
Gyroaverage Effects on Separatrix Reconnectionand Destruction of Shearless Kam Barriers in Non-Twist Systems
Finite Larmor radius (FLR) effects on chaotic transportare studied in a gyro-average Hamiltonian non-twist sys-tem. The Hamiltonian consists of the superposition of anon-monotonic zonal flow and drift waves. We provide ev-idence of the following novel FLR effects: Bifurcation ofzonal flow; Double heteroclinic-homoclinic separatrix re-connection; Suppression of chaotic transport. The thresh-old for the destruction of the shearless KAM curve (com-puted using indicator points) exhibits a fractal dependence
DS11 Abstracts 149
in the Larmor-radius perturbation-amplitude space.
Diego Del-Castillo-NegreteOak Ridge National [email protected]
Julio J. MartinellInstitute of Nuclear ScienceNational Autonomous University of [email protected]
MS31
Transition to Global Transport in Nontwist Area-preserving Maps: Recent Results
Area-preserving nontwist maps are simple models for de-generate Hamiltonian systems that describe, e.g., magneticfield lines in toroidal plasma devices with reversed mag-netic shear profile. As numerically easily accessible sys-tems, these maps can be used to gain understanding ofbasic features of the physical systems modeled, such as thetransition to global transport. Physical transport barri-ers often correspond to shearless invariant tori which canbreak up or be destroyed in the process of separatrix re-connection. I will discuss the current state of the field andpresent some new results.
Alexander WurmDepartment of Physical & Biological SciencesWestern New England [email protected]
MS32
Controlling the Zoo: A Conservative ControlModel for Biomimetic Robots
Abstract not available at time of publication.
Joseph AyersNortheastern [email protected]
MS32
Using Robotic Models to Test Animal Networksand Hypothesized Connections
We have developed controllers for robotic legs based onthe neural mechanisms of intra-leg joint coordination instick insects and cockroaches. Our controllers coordinatethe activity of multiple independent joints via sensory cou-pling to generate stepping and can adaptively transitionbetween distinct behaviors. We are also developing a novelneural-inspired dynamical control architecture based onstable heteroclinic channels that can flexibly and robustlyorchestrate multiple degrees of freedom, and can readilyhandle behavioral hierarchies, temporal decision-making,and learning, and which incorporates the best aspects offinite state machine and central pattern generator (limitcycle) controllers.
Roger QuinnCase Western Reserve UniversityMechanical and Aerospace [email protected]
MS32
Synthetic CPG Controller for Real-time Imple-mentation of Locomotion Activity and Control Sys-
tem in Swimming Lamprey-base Robot
This paper discusses the design of discrete time modelsfor capturing dynamical behavior of spiking neurons andsynapses that shape the dynamical properties of specificneurobiological networks. Such discrete time map-basedneurons and synapses can be configured to implement themajor features of the command neuron, coordinating neu-ron, and the central pattern generator (CPG) organizationof the lamprey nervous system. This approach enables real-time operation of CPG dynamics on a DSP chip.
Nikolai RulkovUniv of California / San DiegoInst for Nonlinear [email protected]
MS32
Implementation of Neuronal Networks for ReactiveAutonomy
To better understand how sensory systems modulate be-havior and demonstrate the advantages of neuronal cir-cuits over algorithmic control, we developed an exterocep-tive sensory suite consisting of an accelerometer, tilt sen-sor, compass and sonar short baseline array (SBA). Givena goal such as a destination the robot will make decisionsreactively, based on its sensory inputs, rather than a pre-determined algorithm. Compensation for impediments bynested exteroceptive reflexes will allow the robot to navi-gate reactively in unpredictable environment.
Anthony WestphalNotheastern University, Marine Science [email protected]
MS33
Applications of Asymptotic Theory to Scroll WaveDynamics
The asymptotic dynamics of scroll waves in reaction-diffusion equations due to small symmetry breaking pertur-bations results in motion equations of string-like objects,the scroll filaments. We compare the asymptotic predic-tions with results of numerical simulations, for two teststudies. Time-periodic delocalized perturbations (resonantdrift) may be considered as a method of low-voltage defib-rillation. Drift due to spatial gradient of parameters hasimportant role in arrhythmogenicity of border zone of my-ocardial ischemia.
Vadim N. BiktashevDept of Mathematical SciencesUniversity of [email protected]
Irina BiktashevaUniversity of [email protected]
Stuart W. Morganformerly University of [email protected]
Narine SarvazyanGeorge Washington [email protected]
150 DS11 Abstracts
MS33
Scroll Wave Break-up and Filament Turbulence
Scroll waves and their associated filaments can becomeunstable through a number of different bifurcations, of-ten leading to turbulent behavior. In this talk, I will givean overview on how different bifurcations can leave theirsignature on the statistical properties of the turbulent dy-namics. For example, one can distinguish between differ-ent instabilities thought to be relevant in the context ofcardiac arrhythmia even if only the surface of a boundedthree-dimensional medium is observable.
Jorn DavidsenDepartment of Physics and AstronomyUniversity of [email protected]
MS33
Interaction of Scroll Waves in the Presence and Ab-sence of External Gradients
We investigate experimentally the interaction of a pairof meandering scroll waves in the excitable Belousov-Zhabotinsky reaction medium. The organising centres ofthe scrolls, the so-called filaments, were originally straight.Two cases are considered: co-rotating and counter-rotatingscroll waves in the presence and absence of a gradient par-allel to the filament. While in the absence of gradients, spo-naneous symmetry breaking occurs and the slower scroll isousted, the situation differs in the presence of a gradeint.Here, wen need to consider the relative sense of rotation.While counterrotating scrolls behave as in the absence ofa gradient (i.e. the slower scroll is expulsed), co-rotatingwaves synchronise and stabilize each other.
Marcus HauserInstitute of Experimental PhysicsOtto-von-Guericke-Universitatmarcus.hauser@physik.uni-magdeburg.de
MS33
Pinning of Scroll Waves in Excitable Systems
I will present an overview of recent results on scroll wavedynamics in excitable reaction-diffusion systems. Exper-imental results from chemical experiments will be com-pared to PDE simulations and curvature flow models. Ouranalyses focus on the motion of the scroll filament whichis the one-dimensional rotation backbone of these three-dimensional structures. Specific examples include solutionsinvolving translating as well as rotating filament motion.
Oliver SteinbockDepartment of Chemistry and BiochemistryFlorida State [email protected]
MS34
Using Mathematical Models of Varying Complex-ity to Study the Great Snowball Earth Events
Geological evidence indicates that at least twice duringthe Neoproterozoic era (∼635 and ∼715 million years ago)there were global glaciations during which Earth’s oceansmay have been covered with O(1 km) thick ice: SnowballEarth events. I will describe mathematical and physicalmodels of a hierarchy of complexity that can be used tounderstand why Snowball Earth events can occur, what
their climate would be like, and how a Snowball Earth canend.
Dorian S. AbbotDepartment of Geophsyical SciencesUniversity of [email protected]
MS34
A Paleoclimate Model of Ice-Albedo Feedback
A model of ice-albedo feedback dating back to Budyko andSellers is combined with computations of the Earth’s or-bital parameters to examine the role of ice-albedo feedbackin the paleoclimate record. The changes in the Earth’sobliquity are shown to be the major driver in both themodel output and the climate record.
Richard McGeheeUniversity of [email protected]
MS34
Relaxations Oscillations in a Simple Ocean-BoxModel Modulated by Zonal Insolation - a PossibleMechanism for Dansgaard-Oeschger Events
The climate of the last 100,000 years experienced severalsudden warming episodes with approximately 1,500 yeardurations. It is generally suggested that freshwater dis-charge from land ice-sheets triggered changes in the stateof the Atlantic meridional circulation, effecting the climate.However many of the features of the climate record re-main unexplained. Using a simple ocean-sea-ice model Ishow that intrinsic oceanic oscillations can be modulatedby zonal insolation to produce a pattern quite similar toproxy records.
Raj SahaUniversity of North [email protected]
MS34
Dynamics of An Energy Balance Model
A 1-dimensional energy balance model was first introducedin late sixties independently by Mihail Budyko (Main Geo-physical Observatory, Russia) and William Sellers (Uni-versity of Arizona). Budyko in particular, introduced anequation that governs the evolution of the one hemispherictemperature distribution, by taking into account the icealbedo feedback phenomenon. In this talk I will summa-rize Budyko’s model and introduce an equation that in-duces the ice line dynamics. Then I will present a resulton the existence of a center stable manifold and some fu-ture directions.
Esther WidiasihDepartment of MathematicsThe University of [email protected]
MS35
Learning Hybrid Controllers from Animal Tracking
I am interested in a constructionist approach to under-standing social animal behavior. By that I mean that Iendeavor to build small “programs’ that fully describe in-
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dividual animals’ method of interaction with their environ-ment. We infer, or learn these programs or models fromobservation of the movement of animals in video. Whenhundreds or thousands of such programs are instantiatedin simulated animal “bodies’ we can assess the accuracyof the models and also use them to predict system levelbehavior.
Tucker BalchSchool of Interactive ComputingGeorgia [email protected]
MS35
Deconfliction in Biological and Bio-inspired Coor-dinated Control
Deconfliction refers to the ability of an autonomous systemto sense and avoid other moving agents. Biological systemsdemonstrate obstacle avoidance and deconfliction capabil-ities when operating in close proximity well beyond thosecurrently achievable by engineered systems. In the workpresented here, algorithms for deconfliction in engineeringsystems based on collision cones are evaluated relative tobiological data.
Kristi MorgansenDept. of Aeronautics and AstronauticsU. of [email protected]
MS35
Reconstruction and Analysis of Individual Dynam-ics in Fish Schools and Mosquito Swarms
This talk will describe ongoing research that seeks to im-prove our understanding of collective behavior in naturalsystems by applying tools from applied mathematics andengineering. We will present (1) new insights on informa-tion transmission via non-verbal signaling obtained usingan automated video-tracking framework to reconstruct full-body trajectories of densely schooling fish; and (2) resultsfor accurately reconstructing the three-dimensional trajec-tories of individual mosquitoes in swarms of An. gambiae,arguably the most deadly animal on earth.
Derek A. Paley, Sachit ButailUniversity of MarylandDepartment of Aerospace [email protected], [email protected]
MS35
Tracking Fish Schools in 2D with Real-time Appli-cations
Real-time tracking of fish enables automated feedback con-trol of stimuli in laboratory fish schooling experiments; thisis particularly significant for experiments designed to bet-ter understand mechanisms of collective behavior. We de-scribe our platform that enables both real-time and off-linevideo-based tracking of fish schools. Our methods includemixture-of-gaussian clustering, head-tail distinction, Hun-garian matching, and unscented Kalman filter tracking.We discuss the estimation from tracked data of group-levelquantities such as polarization and present experimentalresults.
Daniel T. SwainDepartment of Mechanical and Aerospace Engineering
Princeton [email protected]
Naomi E. Leonard, Iain CouzinPrinceton [email protected], [email protected]
MS36
Traveling Waves for Reaction-convection-diffusionSystems
Hyperbolic systems of differential equations with stiffsource terms can be approximated by (smaller) systemswith diffusive terms. This follows from a result of T.P.Liu,explaining why reaction-convection equations possess trav-eling waves. One can add other diffusive terms to such asystem, preserving the nature of the solution, provided theadditional term is dominated by Liu’s diffusion. This is il-lustrated in the context of combustion in a porous medium.
Dan MarchesinInstituto Nacional de Matematica Pura e [email protected]
Alexei A. MailybaevInstitute of Mechanics, Moscow State [email protected]
Julio D. Machado SilvaInstituto Nacional de Matematica Pura e [email protected]
MS36
Long-time Behavior and Approximation of Nonlin-ear Waves
We consider systems of parabolic PDEs which are nonlin-early coupled to a system of hyperbolic PDEs. We ana-lyze the stability of traveling waves in such problems andexplain their numerical approximation with the freezingmethod [Beyn, Thummler 2004], [Rowley et al. 2003]. Theprincipal idea is to reformulate the problem as a partialdifferential algebraic equation using nonlinear coordinates.In numerical examples we show that the analytically pre-dicted rate of convergence can also be observed in compu-tations.
Jens Rottmann-MatthesDepartment of MathematicsBielefeld University, [email protected]
MS36
Stability of Traveling Waves for Parabolic and Par-tially Parabolic Combustion Problems
I will discuss nonlinear stability results for traveling wavesin a class of reaction-diffusion systems that arise in chemi-cal reaction models. The class includes partially parabolicsystems, which require a “spectral stability implies lin-earized stability” result recently proved by the authors.The results are detailed enough to show, for example, thatthe effects of adding some heat or adding some reactant toa combustion front are different.
Anna GhazaryanDepartment of Mathematics
152 DS11 Abstracts
Miami University and University of [email protected]
Yuri LatushkinUniversity of Missouri, [email protected]
Stephen SchecterNorth Carolina State UniversityDepartment of [email protected]
MS36
Traveling Waves in the Buffered FHN System
Calcium waves are widely observed with the free cytoso-lic calcium bound to large proteins that act as calciumbuffers. Therefore it is of physiological importance to in-vestigate the buffering effect on the properties of calciumwaves. Motivated by this, we study traveling waves in thebuffered FHN equation where the free cytosolic calcium isbuffered. This is a joint work with James Sneyd.
Je-Chiang TsaiDepartment of MathematicsNational Chung Cheng University (Taiwan)[email protected]
MS37
Stability Indices for Heteroclinic Networks
This talk will discuss a dynamical invariant - the stabilityindex - that can be used to characterize the local geometryof a basin of attraction. This invariant gives the scalingof the relative measure of a neighbourhood that is in abasin of attraction. It is useful for understanding hetero-clinic attractors in cases where they are Milnor attractors,but not asymptotically stable. The talk will briefly discussan application to simple robust heteroclinic cycles in R4,generalizing previous results of Krupa and Melbourne.
Peter AshwinUniversity of [email protected]
Olga PodviginaInstitute of Earthquake Prediction Theory & [email protected]
MS37
Homoclinic Cycles: Dynamics and Bifurcations
Recent work has shown intricate properties of dynamicsnear heteroclinic networks. Even for networks that are at-tractors, convergence of trajectories to it may occur in com-plicated ways. We discuss two specific examples. The firstexample involves a bifurcation of an asymptotically sta-ble homoclinic cycle to an essentially asymptotically stablehomoclinic cycle. The second example involves switchingdynamics near a homoclinic cycle.
Ale Jan HomburgKdV Institute for MathematicsUniversity of [email protected]
MS37
Switching on a Heteroclinic Network
It is well known that heteroclinic cycles and networks canexist robustly in systems with symmetry. After an in-troduction to dynamics near heteroclinic cycles and net-works, I will consider a particular heteroclinic network indetail. This network exhibits ‘switching between differentsub-cycles. The mechanism for switching is the presence ofspiralling due to complex eigenvalues. Some of the unsta-ble manifolds are two-dimensional; I describe a techniqueto account for all trajectories on those manifolds.
Claire M. PostlethwaiteUniversity of [email protected]
Alastair M. RucklidgeDepartment of Applied MathematicsUniversity of [email protected]
Vivien KirkUniversity of [email protected]
Mary SilberNorthwestern [email protected]
Emily [email protected]
MS37
Universal Computation by Switching in NeuralNetworks
Dynamic switching among saddles persistently emerges ina broad range of systems and may reliably encode informa-tion in neural networks. Their computational capabilities,however, are far from being understood. Here, we showthat system inhomogeneities naturally yield controllableswitching in neural networks. Such dynamics genericallyenables to compute all basic logic operations by enteringinto switching sequences in a controlled way. thus offeringa flexible new kind of universal computation.
Fabio Schittler NevesMax Planck Institute for Dynamics and [email protected]
Marc TimmeMax Planck Institut for Dynamics and Self-OrganizationGoettingen, [email protected]
MS38
Stochastic Inference of Cell Migration Phenotypes
Here a methodology for quantification of cell migrationphenotypes is developed. Fitting of a stochastic model toexperimentally observed cell tracks leads to estimation ofparameters characterizing velocity and persistence of orien-tation. This method is applied to explore the role of RhoG,a Rho GTPase. We conclude that RhoG knock down cellsare less efficient at exploring their environment and that
DS11 Abstracts 153
their are two states of migratory behavior.
Richard AllenUniversity of North Carolina, Chapel [email protected]
Christopher WelchUniversity of North [email protected]
Klaus HahnUniversity of North Carolina at Chapel [email protected]
Tim ElstonUniversity of North [email protected]
MS38
A General Markov Model for Pole Formation
A classic mechanism of symmetry breaking used for mod-eling pole formation on the surface of cells is via the Tur-ing models, which is a class of nonlinear reaction-diffusionsystems. Solutions to the full nonlinear system are usu-ally difficult to obtain and one must resort to a numericalintegration. We explore a set of stochastic models of poleformation which capture the essential biological details andalso have the property of being amenable to mathematicalanalysis.
Badal JoshiDuke [email protected]
Scott McKinleyUniversity of [email protected]
Michael C. ReedDuke [email protected]
MS38
Analytical Theory for Cascade Formation in Clus-tered Scale-Free Neuronal Network Model
We will present a second order calculation with explicitreference to clusters (triangles) to characterize the suscep-tibility of a network of stochastic integrate-and-fire neuronsto giant cascading events as a function of the underlyingnetwork and dynamical parameters. The network is scale-free with a high degree of clustering. The results of thecalculation are in excellent agreement with direct numer-ical simulations, and markedly superior to a calculationassuming a tree-like network.
Katherine NewhallRensselaer Polytechnic [email protected]
Peter R. KramerRensselaer Polytechnic InstituteDepartment of Mathematical [email protected]
Gregor KovacicRensselaer Polytechnic Inst
Dept of Mathematical [email protected]
Max ShkarayevCollege of William and MaryDept. of Applied [email protected]
David CaiShanghai Jiao Tong University, ChinaCourant institute, New York University, [email protected]
MS38
Collective Dynamics of Processive Molecular Mo-tors
Internal to biological cells is an intricate transport appa-ratus, which consists of a cytoskeletal network of thin fil-aments called microtubules and proteins called processivemolecular motors. These motors move in a directed fashionalong the microtubules while generating sufficient force totow biomolecular cargos. While experimentalists and theo-reticians have had good success in describing the dynamicsof a single motor with an attached cargo, there is con-siderable debate regarding how multiple motors cooperateand/or interfere with each other when they are attachedto the same cargo. In this talk we discuss an SDE modelfor this scale of intracellular transport and present somefindings which resolve one of the outstanding mysteries en-countered by experimentalists: common sense says thereare multiple motors acting in concert, but certain mea-surements seem to imply that only one motor is workingat a time.
Avanti AthreyaDuke [email protected]
John FricksDept of StatisticsPenn State [email protected]
Pete KramerRensselaer Polytechnic [email protected]
Scott McKinleyUniversity of [email protected]
MS39
Ensemble Modeling of Human Immune Responseto IAV Infection
We present an ensemble model of the human immune re-sponse to influenza A virus infection, consisting of an ODEsystem with probability distribution on parameters reflect-ing the goodness of fit to empirical data. Ensemble modelsof biological systems provide probabilistic predictions ofthe dynamics that approximate the variability of responseamong individuals. We used the model to compute prob-abilistic estimates on the trajectories of the immune re-sponse, duration of disease, maximum tissue damage, like-lihood of rebound of disease and superspreaders. We foundthat the strength, duration and time of initiation of antivi-ral treatment have significant effects on treatment benefits.
154 DS11 Abstracts
Baris HanciogluVirginia [email protected]
Gilles ClermontUniversity of [email protected]
David SwigonDepartment of MathematicsUniversity of [email protected]
MS39
The Dynamics of Foreign Body Reaction Models in2-dimensions
The foreign body reactions model the network of immuneand inflammatory reactions of human or animal bodies toforeign objects placed in tissues. This study focuses onkinetics-based predictive models in order to analyze com-plex reactions of various cells/proteins and biochemicalprocesses and to understand transient behavior. Computa-tional models based on continuum and multi-scale methodswere constructed to investigate the time dynamics as wellas spatial variations. Several numerical examples will bediscussed.
Jianzhong SuUniversity of Texas at ArlingtonDepartment of [email protected]
MS39
A Mathematical Model of Ischemic Wound Healing
Chronic wounds represent a major public health problemaffecting 6.5 million people in the United States. Ischemia,primarily caused by peripheral artery diseases, represents amajor complicating factor in chronic wound healing. In thistalk, we present a mathematical model of ischemic dermalwounds. The model consists of a coupled system of partialdifferential equations in the partially healed region, withthe wound boundary as a free boundary. The extracellu-lar matrix (ECM) is assumed to be viscoelastic, and thefree boundary moves with the velocity of the ECM at theboundary. The model equations involve the concentrationof oxygen, PDGF and VEGF, the densities of macrophages,fibroblasts, capillary tips and sprouts, and the density andvelocity of the ECM. Simulations of the model demonstratehow ischemic conditions may limit macrophage recruitmentto the wound-site and impair wound closure. The resultsare in general agreement with experimental findings.
Chuan XueOhio State [email protected]
Avner FriedmanDepartment of Mathematics, Ohio State [email protected]
Chandan SenOhio State University Medical [email protected]
MS40
Uncertainty and Sensitivity Analysis in BuildingModels
As building energy modeling evolves, the number of pa-rameters used to define these models continues to grow.There are numerous sources of uncertainty in these param-eters, and past efforts have used uncertainty and sensitivityanalysis to quantify how uncertainty in tens of parametersinfluence predicted results. We present work where we in-crease the size of analysis by two orders of magnitude, anddecompose the sensitivity pathways to identify how uncer-tainty flows through the dynamics.
Bryan [email protected]
MS40
Model-based Failure Mode Effect Analysis in HighPerformance Buildings
System failure modes are the mechanisms that can causesystem performance loss, such as failed valves or dampersin buildings causing excess energy consumption. Wholebuilding energy models combined with rapid Monte-Carlosimulation can be extended to analyze building systemsand controls failure modes, for prioritization. Model con-struction must partition failure modes that cannot simul-taneously occur, and delimit the failure modes to their oc-currence rates. The result is an order 1/n analysis, ratherthan 2n.
Kevin OttoRobust Systems and [email protected]
MS40
Lagrangian Coherent Structures Based Analysis ofBuilding Airflows
Passive building cooling and heating systems exploit spa-tial temperature stratification and buoyancy to reduce en-ergy consumption; however the 3D inhomogeneous thermo-airflow patterns that arise are difficult to analyze. In thistalk we demonstrate the use of dynamical system methodsto extract Lagrangian Coherent Structures to systemati-cally characterize such spatiotemporally varying patterns,and assess their impact on occupant comfort and energyconsumption. We illustrate this in several building exam-ples comparing conventional and passive systems.
Amit SuranaSystem Dynamics and OptimizationUnited Tecnologies Research Center (UTRC)[email protected]
Sunil Ahuja, Satish NarayananUnited Technologies Research [email protected], [email protected]
MS40
Challenges and Numerical Consideration in Build-ing Energy Modeling
Building energy and control systems lead to multi-physics,multi-scale heterogeneous complex systems. The underly-ing equations are nonlinear systems of ordinary differential
DS11 Abstracts 155
equations, partial differential equations and algebraic equa-tions with continuous and discrete states. Modeling, sim-ulation and analysis of such systems pose new challengesas systems become increasingly integrated. We present re-cent research in the development of tools that support themodeling, simulation and analysis of such systems.
Michael [email protected]
Wangda ZuoLawrence Berkeley National [email protected]
MS41
Ribosome Traffic During Protein Synthesis
I will present a description of the process of mRNA transla-tion based on Petri Nets. This approach has the advantageof yielding analytic solutions for the realistic case of mR-NAs consisting of a inhomogeneous sequence of codons,in contrast to the totally asymmetric exclusion process(TASEP) commonly used to describe translation. The so-lutions obtained with this framework based on the MaxPlus algebra will be discussed and compared with the onesobtained with the TASEP.
David BroomheadThe University of ManchesterApplied [email protected]
MS41
Robustness of Circadian Clocks to Daylight Fluc-tuations: Hints from Picoeukaryote OstreococcusTauri
Circadian clocks are genetic oscillators keeping time inmany organisms, which synchronize to the day/night cycleby sensing ambient light. However, daylight fluctuationscould randomly reset the clock. Modeling the clock of thegreen unicellular alga Ostreococcus tauri has uncovered adynamical solution to this problem. Coupling to light oc-curs during specific time intervals, where the oscillator isunresponsive. Thus, coupling is ineffective when clock ison time but resets it when out of phase.
Quentin Thommen, Benjamin Pfeuty, Pierre-EmmanuelMorantPhLAM/Universite Lille 1, [email protected],[email protected],[email protected]
Florence CorellouObservatoire Oceanologique de Banyuls (UPMC/CNRS)[email protected]
Francois-Yves BougetUMR CNRS/Paris 6 7628Observatoire oc’eanologique de Banyuls/mer, [email protected]
Marc LefrancPhLAM/Universite Lille I,[email protected]
MS41
Identifiability and Observability Analysis for Ex-perimental Design in Nonlinear Dynamical Modelsin Systems Biology
Modeling of molecular reaction networks by ODEs facesdifficulties when estimating model parameters from incom-plete and noisy experimental data. By means of an appli-cation from cell biology [Becker et al., 2010] we present anapproach that uses the profile likelihood to detect bothstructural and practical non-identifiabilities and investi-gates their influence on the model dynamics [Raue et al.,2009]. The approach also allows to design new experimentsthat resolve non-identifiabilities and to derive confidenceintervals.
Andreas RauePhysics Institute, University of [email protected]
Clemens KreutzUniversity of FreiburgInstitute of [email protected]
Ursula KlingmuellerGerman Cancer Research Center, [email protected]
Jens TimmerUniversity of FreiburgDepartment of [email protected]
MS41
Translational Regulation of Gene Expression
We present a stochastic model that captures the essentialsteps of the process of translation. In contrast to oversim-plified models, it crucially considers the two main time-scales of the biological process. Using this model, we cal-culate the translation rate of the whole genome of S. cere-visiae depending on the initiation rate of ribosomes. Thisallows us to classify proteins according to their transla-tional dynamics and relating them to their biological func-tion.
M. Carmen RomanoInstitute for Complex Systems and Mathematical BiologyandInstitute of Medical Sciences, University of Aberdeen, [email protected]
Luca CiandriniInstitute for Complex Systems and Mathematical BiologyUniversity of Aberdeen, [email protected]
Ian StansfieldInstitute of Medical SciencesUniversity of Aberdeen, [email protected]
MS42
Characterisitc Lyapunov Vectors: CriticalOverview and State of the Art
Characteristic Lyapunov vectors (CLVs) convey the infor-
156 DS11 Abstracts
mation of the tangent dynamics of a system: they are in-trinsic, independent of the scalar product, and covariantunder time evolution. However, until recently, it was notknown how to compute CLVs efficiently in large systems.In this talk I will review the methods recently available tocompute CLVs as well as the applications of these vectorsto a variety of practical and theoretical problems.
Diego PazoInstituto de Fisica de Cantabria, [email protected]
MS42
Lyapunov Analysis and Hyperbolicity of ExtendedDynamical Systems
Lyapunov exponents and vectors are important charac-teristics of nonlinear dynamical systems. Recently sev-eral efficient algorithms are proposed for the calculationof the so-called covariant/characteristic Lyapunov vectors(CLVs) and the associated instantaneous Lyapunov expo-nents, which allows to probe the hyperbolicity of high di-mensional dynamical systems. Our recent results on thehyperbolicity of dissipative partial differential equationswill be reviewed and the relation to effective degrees offreedom of those infinite dimensional systems will be dis-cussed.
Hong-Liu YangInstitute of Physics, Chemnitz University of [email protected]
Gunter RadonsChemnitz University of [email protected]
MS42
Structure and Dynamic Localization of Character-istic Lyapunov Vectors in Anharmonic HamiltonianLattices
We study the scaling behavior of Lyapunov vectors (LV)of two different one-dimensional Hamiltonian lattices. Thecharacteristic LVs exhibit qualitative similarities withthose corresponding to dissipative lattices, but the scalingexponents are different and seemingly non-universal. Incontrast, backward LVs present approximately the samescaling exponent for both models, suggesting that it is aproduct of the imposed orthogonality. We employ a ’bit re-versible’ algorithm that largely reduces computer memorylimitations.
Mauricio Romero-BastidaInstituto Politecnico NacionalEscuela Superior Ingenieria Mecanica y Electrica [email protected]
MS42
Efficient Computation of Characteristic LyapunovVectors in Spatially Extended Systems
An efficient, norm-independent method for constructingthe n most rapidly growing Lyapunov vectors (LVs) fromn − 1 leading forward and n leading backward asymptoticsingular vectors (SVs) is proposed. In spatially extendedsystems, the number of required SVs, 2n − 1, is typically
much less than the dimensionality of the system. The LVsso constructed are invariant under the linearized flow inthe sense that, once computed at one time, they are de-fined, in principle, for all time through the tangent linearpropagator.
Christopher L. WolfeClimate, Atmospheric Science, and PhysicalOceanographyScripps Institution of Oceanography, [email protected]
Roger SamelsonCollege of Oceanic and Atmospheric SciencesOregon State [email protected]
MS43
Self-organized Criticality in Adaptive Neural Net-works
Adaptive network combine topological evolution of a com-plex network and dynamics in the network nodes. Theyexhibit several dynamical phenomena, including highly ro-bust self-tuning to critical states corresponding to phasetransitions. Important real world examples of adaptivenetworks are biological neural networks. In this talk I willpresent data providing evidence for critical dynamics in pa-tients. The self-tuning to the critical state is then analyzednumerically and analytically. Finally, I argue that critical-ity may be crucial for neural information processing andoutline technical applications for adaptive self-tuning.
Thilo GrossMax-Planck Institute for Physics of Complex [email protected]
MS43
Criticality and Dynamic Network Reconfigurationin Human Brain fMRI and MEG Recordings
Self-organized criticality is an attractive model for braindynamics. We found evidence in fMRI and MEG data thathuman brain systems exist in this state, characterized bypower-law distributions of both prolonged periods of phase-locking, and of large rapid changes in global synchroniza-tion. Graph theoretical analysis of such reconfigurationsduring a working memory task revealed that cognitive ef-fort transiently breaks up functional modules resulting ina network which is more integrated over long distances.
Manfred G. KitzbichlerBehavioural and Clinical Neuroscience InstituteUniversity of Cambridge, [email protected]
MS43
Predicting Criticality and Dynamic Range in Com-plex Networks: Effects of Topology
The effect of network structure on the dynamics ofnetwork-coupled discrete-state excitable elements understochastic external stimulus can be understood throughspectral properties of the weighted network adjacency ma-trix. We show that when the adjacency matrix has largesteigenvalue equal to one, dynamics will be in a critical state,maximizing the dynamic range of stimulus to response.Further analysis predicts that networks with more homo-
DS11 Abstracts 157
geneous degree distributions allow a higher achievable dy-namic range at criticality.
Daniel LarremoreApplied MathematicsUniversity of Colorado at [email protected]
MS43
Neuronal Avalanches and Optimized InformationProcessing in Cortical Neural Networks
Rapidly growing empirical evidence supports the hypothe-sis that the cerebral cortex operates in a dynamical regimenear the critical point of a phase transition. This raises aquestion: What benefits are endowed to organisms whosebrain circuits operate near criticality? We present experi-ments on living neural networks which suggest that threeaspects of information processing are optimized at critical-ity: 1) dynamic range, 2) information transmission, and 3)information capacity.
Woodrow L. ShewNIH/NIMH, 35 Convent Dr.Bethesda, MD, USA [email protected]
MS44
Spiking and Bursting in an Autonomous Model ofMouse Ventricular Myocytes
Comprehensive model of mouse ventricular myocytes withsmall constant input current is demonstrated to generatecomplex spiking and bursting oscillations. We examine thebifurcations underlying the transitions between the steadystates and oscillatory activities as the magnitude of theconstant current is varied. Inactivation of the fast Na+
current is a major determinant for both spiking and burst-ing activities. This self-sustained activity is considered asa trigger of non-reentrant arrhythmia in the mouse heart.
Vladimir E. BondarenkoDepartment of Mathematics and StatisticsGeorgia State [email protected]
Andrey ShilnikovNeuroscience Institute and Department of MathematicsGeorgia State [email protected]
MS44
Alternans and Nonlinear Dynamics in Cardiac Tis-sue
Many cardiac arrhythmias contain are associated withcomplex spatiotemporal dynamics. This talk will describethe nonlinear dynamics of electrical waves in the heart, in-cluding states with planar waves, single spiral/scroll waves,and multiple interacting waves, together with how they aremodeled mathematically. Special attention will be givento alternans, an arrhythmia characterized by a beat-to-beat variation in cellular response that can produce com-plicated patterns. Challenges and opportunities associatedwith this system will be discussed.
Elizabeth M. CherryCornell UniversityDepartment of Biomedical Sciences
Flavio H. FentonDepartment of Biomedical SciencesCornell [email protected]
MS44
Temperature Effects on Spatial Patterns of CardiacAlternans
Ventricular tachyarrhythmias result from disruptions tothe heart’s rhythm and are associated with ventricular fib-rillation. One such arrhythmia is alternans, in which con-stant pacing at a rapid period produces a period-doublingbifurcation resulting in alternating long-short electrical re-sponses and complex spatial patterns. We characterizedspatial alternans properties using optical mapping record-ings of isolated canine ventricles at four different temper-atures over a range of periods. We show how complexalternans patterns develop and change with temperature.
Alessio GizziUniversity Campus Bio-medico of [email protected]
Elizabeth M. CherryCornell UniversityDepartment of Biomedical [email protected]
Stefan LutherMax Planck Institute for Dynamics and [email protected]
Simonetta FilippiUniversity Campus Bio-Medico of Rome, ItalyICRA University of Rome, La Sapienza, [email protected]
Flavio FentonCornell [email protected]
MS44
Spatio-Temporal Dynamics of Alternans in theHeart
Alternans of action potential duration is a herald for life-threatening ventricular arrhythmias. In isolated myocytes,the appearance of alternans can be predicted by analyz-ing the restitution properties of periodically paced cardiactissue. However, the dynamical behavior of whole heart ismore complex due to presence of spatial component. Weinvestigated the organization and evolution of alternans inisolated rabbit hearts using high-resolution optical map-ping, and identified the mechanisms of spatially concordantand discordant alternans formation.
Alena TalkachovaUniversity of [email protected]
MS45
Factors Controlling the Stability of the Sea Ice
158 DS11 Abstracts
Cover
The contrast in surface albedo between sea ice and openocean suggests the possibility of multiple climate statesand associated nonlinear thresholds during sea ice retreat.We investigate the factors controlling such a possibility byperforming a bifurcation analysis over all of the parame-ters in an idealized single-column model. The results arephysically interpreted and then compared with simulationscarried out with more comprehensive models.
Ian EisenmanCalifornia Institute of TechnologyDivision of Geological and Planetary [email protected]
MS45
Rapid Sea Ice Loss in Climate Model Simulationsof a Changing Arctic
Climate models project transitions to perennially ice-freeArctic conditions that are punctuated by instances of rapidsea ice loss. These rapid ice loss events (RILES) are ac-companied by dramatic increases in cloud cover and warm-ing. Here we discuss the forcing and feedbacks associatedwith RILEs. Additionally, we analyze a series of climatemodel integrations to explore the potential bifurcation andhysteresis of perennial sea ice loss simulated by the Com-munity Climate System Model.
Marika HollandNational Center for Atmospheric [email protected]
MS45
Sea Ice as a Discrete Map
We treat the Semtner-0-layer thermodynamical sea icemodel as a discrete map. We show that under an ad-ditional external heat flux – the bifurcation parameter –Multi-Year-Cycles (MYC) can appear due to discontinuity-induced- and flip-bifurcations leading to a period-addingcascade with interspersed chaotic behaviour. We discussthe robustness of these MYC when subject to noisy forc-ings and why they may mask sea ice decline in winter.
Kay HuebnerMax-Planck-Institute for [email protected]
MS45
Bifurcation Analysis of a Low-order Model of Arc-tic Sea Ice
Eisenman and Wettlaufer (2009) used energy balance con-siderations to introduce a conceptual ODE model for in-vestigating bifurcations associated with seasonal Arctic seaice loss, as greenhouse gas levels increase. We examine aversion of their model that allows us to derive an explicitPoincare return map describing the average Arctic sea icethickness from one year to the next. The range of possi-ble bifurcation behavior for fixed points of the map is thendetermined analytically.
Mary C. SilberNorthwestern UniversityDept. of Engineering Sciences and Applied [email protected]
Dorian S. AbbotDepartment of Geophsyical SciencesUniversity of [email protected]
Raymond T. PierrehumbertGeophysical Sciences Dept.University of [email protected]
MS46
The Pearling Instability in Polymer Electrolyte So-lutions
Recently, it has been shown that the formation of struc-tures in polymer electrolyte solutions can be modeled byregularizing the Canham-Helfrich free energy into a finite-width phase field model. This regularization – called thefunctionalized Cahn-Hilliard Energy (FCHE) – allows fordouble layer, i.e. bi-layer, interfaces whose thickness scaleswith an asymptotically small parameter. If the double-well potential W appearing in the FCHE is symmetric,these double layer structures can be shown to be stable asnetwork patterns of the mass-preserving gradient flow as-sociated to the FCHE. However, in two space dimensions,as the well W is made asymmetric, the bi-layer patternsevolve into a ’pearled network’ – as will be discussed inthis talk.
Arjen DoelmanUniversity of [email protected]
Greg HayrapetyanDepartment of MathematicsMichigan State [email protected]
Keith PromislowMichigan State [email protected]
MS46
Geometric Evolution of bi-layers in the Function-alized Cahn-Hilliard Equation
The functionalized Cahn-Hilliard energy (FCH) is a novelhigher-order energy that serves as a model for network for-mation in solvated, functionalized polymers. Leading or-der minimizers of this energy include new bi-layer solutionswith homoclinic cross sections. An overview of the reduc-tion of the gradient flow of (FCH) to the sharp interfaceevolution of these bi-layers is presented.
Gurgen HayrapetyanMichigan State [email protected]
MS46
Energetic Variational Approaches in Ionic Fluidsand Ion Channels
Ion channels are key components in a wide variety of bi-ological processes. The selectivity of ion channels is thekey to many biological process. Selectivities in both cal-cium and sodium channels can be described by the reducedmodels, taking into consideration of dielectric coefficientand ion particle sizes, as well as their very different pri-
DS11 Abstracts 159
mary structure and properties. These self-organized sys-tems will be modeled and analyzed with energetic varia-tional approaches (EnVarA) that were motivated by classi-cal works of Rayleigh and Onsager. The resulting/derivedmultiphysics-multiscale systems automatically satisfy theSecond Laws of Thermodynamics and the basic physicsthat are involved in the system, such as the microscopic dif-fusion, the electrostatics and the macroscopic conservationof momentum, as well as the physical boundary conditions.In this talk, I will discuss the some of the related biological,physics, chemistry and mathematical issues arising in thisarea.
Chun LiuPenn. State UniversityUniversity Park, [email protected]
MS46
The Dynamics and Stability of Localized Spot Pat-terns for the Gray-Scott model in Two Dimensions
The dynamics and stability of multi-spot patterns tothe Gray-Scott (GS) reaction-diffusion model in a two-dimensional domain is studied in the singularly perturbedlimit of small diffusivity ε of one of the two solution com-ponents. A hybrid asymptotic-numerical approach basedon combining the method of matched asymptotic expan-sions with the detailed numerical study of certain eigen-value problems is used to predict the dynamical behaviorand instability mechanisms of multi-spot quasi-equilibriumpatterns for the GS model in the limit ε → 0. For ε → 0,a quasi-equilibrium k-spot pattern is constructed by repre-senting each localized spot as a logarithmic singularity ofunknown strength Sj for j = 1, . . . , k at unknown spotlocations xj ∈ Ω for j = 1, . . . , k. A formal asymp-totic analysis is then used to derive a differential alge-braic ODE system for the collective coordinates Sj andxj for j = 1, . . . , k, which characterizes the slow dynam-ics of a spot pattern. Phase diagrams in parameter spacefor instabilities of the multi-spot pattern due to spot self-replication, spot oscillation, and spot annihilation, are ob-tained. The asymptotic results are validated from full nu-merical simulations.
Michael WardDepartment of MathematicsUniversity of British [email protected]
Wan ChenOxford Centre Collaborative Applied Mathematics,Oxford [email protected]
MS47
Applications of Piecewise Isometries in ElectronicEngineering
In this talk, I shall mention examples of electronic cir-cuits whose dynamics can be described by a class of two-dimensional discontinuous mappings known as piecewiseisometries (PWIs). In at least two of the examples, realismdictates that the models be dissipative, which leads directlyto contraction in the underlying PWI. The result provedin ‘Piecewise contractions are asymptotically periodic’, HBruin & J H B Deane, Proc AMS 137 4 pp 1389–1395(2009), shows that the dynamics of a system described bya piecewise contraction cannot be other than eventually pe-
riodic, although the possibility of the co-existence of manydifferent periodic solutions complicates the picture. Theobvious (difficult) next question is: can we say anythingabout the periodic solutions exhibited by a given PWI?This question will be discussed in the talk, with referenceto computations concerning the dynamics of the ‘contract-ing Goetz map’.
Jonathan DeaneDepartment of MathematicsUniversity of [email protected]
MS47
Singularities of Invertible Planar Piecewise Rota-tions
The purpose of this talk is to provide a brief overviewon the recent results on the properties of the singulari-ties of 2-dimensional invertible piecewise isometric dynam-ical systems in general, and then report some new resultsfor the special case in which the dynamics is the iterationof piecewise rational rotations. First, the speaker reviewshis recent results about the classification of the singulari-ties of 2-dimensional invertible piecewise isometries and theproperties of each class. He classified the afore-mentionedsingularities into three types, among which the first typeis removable, the second type is innocuous, and only thethird type contributes to the intricate singularity structurethat often exhibits chaos and riddling. The classificationwas done based upon the geometrical properties of the sin-gularities. The core issue here is how these distinct geo-metrical properties lead to different dynamical behaviors.Afterwards, he will discuss some new results, namely, thepartial converses of the first set of results, under the restric-tion that the piecewise isometric dynamics consists only ofthe rational rotations.
Byungik KahngUniversity of Minnesota at [email protected]
MS47
Interval Exchange Discontinuity Growth andGroup Actions
An interval exchange transformation (IET) is a piecewiseisometry of the unit interval. An IET is determined by afinite partition of the unit interval into subintervals anda permutation that describes how the subintervals are re-ordered by the map. For a given IET f , the number of dis-continuities of iterates fn is either bounded or exhibits lin-ear growth as a function of n; no sublinear but unboundedgrowth rates can occur. This dichotomy in growth rateshas various applications to the algebraic properties of thegroup of all IETs; for instance, it is shown that IET groupsdo not possess distortion elements, a complete classificationof centralizers in the IET group is given, and the automor-phism group of the IET group is computed.
Chris NovakDepartment of Mathematics and StatisticsUniversity of [email protected]
MS47
Dynamics and Applications of Piecewise Isometries
This talk introduces the dynamics of piecewise isometries
160 DS11 Abstracts
(PWIs) and discusses some features which are relevant toapplications. As a particular example, we consider themixing properties of PWIs, which are fundamentally differ-ent from the stretching and folding mechanism of familiarchaotic advection. As a physical example we consider mix-ing of granular materials. Simulations connect the PWItheory with experiments and demonstrate how cutting andshuffling contributes to increasing interfacial boundaries,leading to effective mixing.
Rob SturmanUniversity of [email protected]
MS48
Connection Between Discrete Stochastic Cell-based Models and Nonlinear Diffusion Equations
In this talk a connection will be described between discretestochastic models describing microscopic motion of fluctu-ating cells in chemotactic field, and macroscopic nonlineardiffusion equations describing dynamics of cellular density.Cells move towards chemical gradient with their shapesrandomly fluctuating. Nonlinear diffusion coefficient willbe shown to depend on cellular volume fraction preventingcollapse of cellular density in finite time. This makes suchequations much more biologically relevant then earlier in-troduced systems. A very good agreement will be shownbetween Monte Carlo simulations of the microscopic cel-lular Potts model and numerical solutions of the macro-scopic nonlinear diffusion equations for relatively large cel-lular volume fractions. Combination of microscopic andmacroscopic models were used to simulate growth of struc-tures similar to early vascular networks. In the secondhalf of the talk, a connection will be demonstrated be-tween a microscopic one dimensional cell-based stochas-tic model of reversing non-overlapping self-propelled rodsand a macroscopic nonlinear diffusion. Boltzmann-Matanoanalysis will be used to determine the nonlinear diffusioncoefficient corresponding to the specific reversal frequency.Periodic reversals of the direction of motion in systemsof self-propelled rod shaped bacteria enable them to ef-fectively resolve traffic jams formed during swarming andmaximize their swarming rate.
Mark AlberUniversity of Notre [email protected]
MS48
Derivation of SPDEs for Correlated Random Walksand SDEs for Sunspot Activity
Stochastic generalizations of correlated random walk mod-els, specifically, the telegraph equation in one dimensionand the linear transport equation in two dimensions, arederived and tested against Monte Carlo calculations. Inaddition, SDEs are derived for sunspot activity. Similari-ties are found between the SDE model and sunspot data.
Edward J. Allen, Ummugul BulutTexas Tech UniversityDepartment of Mathematics and [email protected], [email protected]
Elife DoganDepartment of Mathematics and StatisticsTexas Tech University
Chisum HuffTexas Tech UniversityDepartment of Mathematics and [email protected]
MS48
An Overview of Stochastic Dynamics
The talk will survey results from random dynamical sys-tems, mostly in the setting of discrete time dynamical sys-tems, and, in particular, recent developments on the ther-modynamic formalism for random transformations. As akey example, I present an application from neuroscience,where random input produces power laws and a behavioras for branching processes.
Manfred DenkerPenn State [email protected]
MS48
Impact of Noise on Invariant Manifolds
Invariant manifolds are essential geometric tools for under-standing deterministic dynamical systems. For stochasticdynamical systems, however, invariant manifolds are quitedelicate objects. Random invariant manifolds are sample-dependent geometric objects, but they are not easy to begeometrically visualized or numerically computed. To bet-ter understand random invariant manifolds and thus uti-lize them as building blocks to decode stochastic dynamics,we present a method for approximating random invariantmanifolds when noise is small. This method provides atool for quantifying the impact of small noise on invariantmanifolds, and thus shed lights on describing stochasticdynamics.
Jinqiao DuanIllinois Institute of [email protected]
MS49
Time Averaged Observables in Dynamical SystemAnalysis: An Overview
A part of the operator-theoretic analysis of dynamical sys-tems includes studying how observables, i.e., functionson the state space, evolve with dynamics of the system.Recording only averaged values of observables along theevolution provides us with parsimonious amount of datathat can contain a wealth of information about geometry ofthe state space objects. The talk will provide an overviewof concepts ranging from theory to simulations and appli-cations of time-averaged observables.
Marko BudisicDepartment of Mechanical EngineeringUniversity of California, Santa [email protected]
MS49
Convergence of Long Time Numerical Averages ofSDEs
I will present a different take the analysis showing that thestationary measure of a large class of stochastic numerical
DS11 Abstracts 161
methods converges to that of the underlying SDE. In routeI will show that the numerical time averages are in factclose the the underlining stationary measure. These resultsextend and streamline some classical results of D. Talay.this is joint work with Andrew Stuart and M. Tretyakov.
Jonathan C. MattinglyDuke [email protected]
MS49
Variations on a Harmonic Analysis and ErgodicTheory Based Method for Analyzing Fluid Flows
The ergodicity defect is a technique for capturing both(1)the extent to which a flow/system deviates from ergod-icity and (2)how this deviation depends on scale. Whenthis analysis is done in terms of Haar wavelets, the tech-nique relates to physical notions of average residence timesin subdomains of the flow. Although, the Haar waveletis beneficial in that it allows this intuition-building per-spective, it is only one type of harmonic that can serve asan analyzing function/observable in the ergodicity defectmethod. We generalize the ergodicity defect both in termsof different harmonics - e.g., other multiresolution analysiswavelets - and in the context of a variety of systems andthen consider the usefulness of these variations.
Sherry ScottDepartment of MathematicsMarquette [email protected]
MS49
Shadowing the Trajectories of Molecular Dynamics
An open theoretical problem is to explain the apparentreliabilty of long trajectories in molecular dynamics simu-lations. The difficulty is that individual trajectories com-puted in molecular dynamics are accurate for only shorttime intervals, whereas useful information can be extractedfrom trajectory averages of very long simulations. One con-jecture is that numerical trajectories are shadowed by exacttrajectories: that is, for every numerical trajectory thereis an exact trajectory with different initial conditions thatremains close to the numerical trajectory over long time in-tervals. I will demonstrate for a simple yet representativemolecular dynamics system that long numerical trajecto-ries are not shadowable, and discuss what the implicationsfor interpreting the results of simulations. This is jointwork with Wayne Hayes.
Paul TupperDepartment of MathematicsSimon Fraser [email protected]
MS50
Dynamics of Hepatitis B Virus Infection: WhatCauses Viral Clearance?
Hepatitis B virus infects liver cells, leading to acute (short-term) infection or chronic (permanent) liver disease. Theimmune systems responses to this infection either cure orkill infected cells, but the individual effect of each responseon infection outcome remains uncertain. A better under-standing of these effects could guide treatment options. Inthis work, we consider models of hepatitis B infection, us-ing stability analyses and simulations to examine the roles
of each immune response.
Anne CatllaWofford CollegeDept. of [email protected]
Stanca CiupeDepartment of MathematicsUniversity of [email protected]
Jonathan FordeHobart and William Smith [email protected]
David G. SchaefferDepartment of MathematicsDuke [email protected]
MS50
Moving the Head: The Donderian Way
Donderian head movements always satisfy the constraintthat the axis of head rotation has a small tortional compo-nent. Starting from data of human head movement, in thistalk we present a best fit surface. Up to rotation and trans-lation of this surface, we study to what extent this surfaceresembles the classically studied Fick gimbals. We finishup our presentation talking about the associated geodesicsand the optimal head movement trajectories.
Bijoy K. GhoshDepartment of Mathematics and StatisticsTexas Tech University, Lubbock, TX , [email protected]
MS50
Modeling the Effects of Systemic Cortisol on theWound Healing Process
During the wounding healing process many complex in-teractions occur between fibroblasts and immune media-tors. These interactions determine whether or not thewound will heal. To better understand these dynamics,we have developed a system of differential equations mod-eling the dynamics between local fibroblast and immunecells and the systemic mediator Cortisol. Using this model,we focused on the accumulation of collagen in an oxygen-deprived wound (diabetes) with and without trauma (highcortisol levels).
Angela M. ReynoldsDepartment of Mathematics and Applied MathematicsVirginia Commonwealth University (VCU)[email protected]
MS50
Using a Mathematical Model to Analyze the Treat-ment of a Mathematical Model of a Wound Infec-tion with Oxygen Therapy
A mathematical model was developed to treat a woundwith a bacterial infection using oxygen therapy. Themodel describes the relationship among neutrophils, bac-teria, oxygen, cytokines, and reactive oxygen species. Aquasi-steady-state assumption was introduced to reduce
162 DS11 Abstracts
the model down systems of two and three equations. Amathematical analysis on the reduced model and simula-tion results will be presented in this talk.
Richard SchugartWestern Kentucky [email protected]
MS51
Reduced-order Models for Control of Building In-door Environment
Lumped thermal airflow models, widely used in wholebuilding simulation tools, are inadequate for capturingthermal stratification that typically arises while using pas-sive, low-energy, heating and cooling systems. Computa-tional fluid dynamics (CFD) on other hand is intractablefor practical design and optimization, and real-time con-trol. We develop reduced-order models, using eigensys-tem realization algorithm, for capturing relevant airflowdynamics, and develop controllers that maintain occupantcomfort while minimizing energy consumption.
Sunil AhujaUnited Technologies Research [email protected]
Amit SuranaSystem Dynamics and OptimizationUnited Tecnologies Research Center (UTRC)[email protected]
Eugene CliffVirginia TechInterdisciplinary Center for Applied [email protected]
MS51
Design Specific Computational Tools for Control ofEnergy Efficient Buildings
Building systems are complex dynamical systems and mod-els of such systems are best described by coupled discrete,ordinary and partial differential equations. Direct high fi-delity simulations are not practical for use in design andcontrol and some type of model reduction must be em-ployed. We discuss this issue and present some examplesof nonlinear systems to illustrate the difficulties that oc-cur in generation reduced order design models of complexsystems.
John A. Burns, Eugene Cliff, Lizette ZietsmanVirginia TechInterdisciplinary Center for Applied [email protected], [email protected], [email protected]
MS51
Optimal Zoning in Building Energy Models
Building energy modeling tools have found widespread usein evaluating the energy consumption of a building de-sign. Despite their capability, spatial zoning approxima-tions, which are currently defined based on equipment lay-out, are made when creating models that influences modelaccuracy. In this work, analysis is presented that evaluatesthe impact of zoning grid choice on predictive capability.Specifically theres focus on new issues that arise due tobuilding designs with both mechanical and natural condi-
tioning.
Michael [email protected]
MS51
Nonlinear Behaviors in Building Ventilation Sys-tems
In building ventilation systems, many nonlinear behaviorscan occur and they can be important to the design andoperation of the building thermal systems. In this pre-sentation, we will provide a few such examples in buildingsimulation, and examining the underlying physics that gov-erns such behaviors in the context of fluid flow and ther-mal transport. We will demonstrate how dynamical systemanalysis can be applied to such systems, and how actual ro-bustness of multiple equilibrium states can be examined,and empirical methods to identify solution multiplicity andanalyze the forming mechanism of different equilibriums incomplex building simulation problems.
Jinchao YuanNexant [email protected]
Leon Glicksmanthe Massachusetts Institute of [email protected]
MS52
Synchronized Genetic Clocks in E. Coli
We describe an engineered gene network with global inter-cellular coupling in a growing population of cells and studyits collective synchronization properties. We use compu-tational modelling to describe quantitatively the periodand amplitude of bulk oscillations. The synchronized ge-netic clock sets the stage for the creation of a macroscopicbiosensor with oscillatory output. Furthermore, it providesa specific model system for the generation of a mechanis-tic description of emergent coordinated behaviour at thecolony level.
Tal DaninoSystems biodynamics LabUniversity of California San [email protected]
Octavio Mondragon-PalominoUCSD, Systems biodynamics [email protected]
Lev S. TsimringUniversity of California, San [email protected]
Jeff HastyDepartment of BioengineeringUniversity of California, San [email protected]
MS52
Bifurcation Theory for Evo-devo
The antero-posterior axis of most animals is patternedby segmentation genes and hox genes during embryonic
DS11 Abstracts 163
growth. I use evolutionary computation to predict thestructure of networks implicated in these processes. Simu-lations suggest sequences of evolutionary events which canbe best characterized at the bifurcation level. Evolvedmodels suggest experimental predictions on network dy-namics and on interconversion of developmental modes be-tween insect species.
Paul FrancoisDepartment of Physics,McGill University, Montreal, [email protected]
MS52
Genetic Oscillations: From Time to Space
To study how genetic oscillators inside single cells interactin biofilms and tissues, we have considered repressilators ona hexagonal lattice. Such systems can be built to exhibitstable oscillations. Commensurability effects however maylead to internal frustration causing symmetry breaking andsolutions of many different phases, or even chaos. Withbi-directed interactions the tissues locally exhibit switch-like behavior. Growing tissues may develop ’defects’, withmutations having then more impact than in ordered tissues.
Mogens Jensen, Sandeep Krishna, Simone PigolottiNiels Bohr Institute, [email protected], [email protected], [email protected]
MS52
How Do Cells Behave as a Collective During Em-bryogenesis? The Role of Cell-cell Interaction
Cell-to-cell communication plays a crucial role for main-taining the homogeneity of a cell group in the embryo.Experimental evidences suggest that the cell populationsize must be above a certain threshold to keep such homo-geneity. However, its theoretical basis has been unknown.In this talk, I present a simple model, which consists ina linear gene cascade and cell-to-cell communication. Themodel reproduces the qualitative features of the experi-mental observations, and shows transcritical bifurcation.
Yasushi SakaInstitute of Medical Sciences, School of Medical SciencesUniversity of [email protected]
Cedric Lhoussaine, Celine KuttlerLIFL, UMR Universite Lille 1/CNRS [email protected], [email protected]
Ekkehard UllnerICSMB, Department of PhysicsUniversity of Aberdeen, [email protected]
Marco ThielUniversity of [email protected]
MS53
Fast and Slow Pulses for the Discrete FitzHugh-
Nagumo Equation
The existence of fast travelling pulses of the discreteFitzHugh-Nagumo equation is obtained in the weak-recovery regime. This result extends to the spatially dis-crete setting the well-known theorem that states that theFitzHugh-Nagumo PDE exhibits a branch of fast wavesthat bifurcates from a singular pulse solution. The keytechnical result that allows for the extension to the dis-crete case is the Exchange Lemma that we establish forfunctional differential equations of mixed type.
Hermen Jan HupkesDepartment of Applied MathematicsBrown [email protected]
MS53
Neutral Mixed Type Functional Differential Equa-tions
We extend the linear Fredholm theory for mixed type func-tional differential equations (with both advances and de-lays) to neutral equations of mixed type. We consider aprototype problem of coupling between two nerve fibersin which a traveling wave assumption results in a systemof neutral type equations. We employ the linear theorydeveloped and local continuation to show existence and in-vestigate the stability of solutions for small values of thecoupling parameter.
Charles LambDepartment of MathematicsUniversity of [email protected]
MS53
Propagation Failure in the Discrete Nagumo Equa-tion
We address the classical problem of propagation failurefor monotonic fronts of the discrete Nagumo equation.For a special class of nonlinearities that support unpinned”translationally invariant” stationary monotonic fronts, weprove that propagation failure cannot occur. We give twoproofs of this result: one is based on the center manifoldreductions and the other one is based on analysis of lin-earized differential advance-delay equations. We show thatthese equations in the singular limit of zero speed possessan infinite-dimensional kernel spanned by Fourier harmon-ics of fronts translations, which are accounted when thestationary front is continued into the traveling one.
Dmitry PelinovskyMcMaster UniversityDepartment of [email protected]
MS53
Nonlinear Stability of Semidiscrete Shocks
The nonlinear stability of Lax shocks is considered forsemidiscrete systems of conservation laws, where the spa-tial coordinate is discrete, while time is continuous. Thekey for nonlinear stability is Green’s functions of the lin-earized problem, which is an ill-posed functional differen-tial equation of mixed type. The goal of this talk is to givebackground information about semidiscrete systems and toillustrate the techniques that allow us to construct Green’s
164 DS11 Abstracts
functions.
Bjorn SandstedeBrown Universitybjorn [email protected]
MS54
Synchronization in Networks with DisconnectedComponents
We study global stability of synchronization in dynamicalnetworks with disconnected components. Each componentis a graph connecting a subnetwork of nodes via one of theindividual systems variables. The graphs correspondingto the couplings via different variables are disconnected,however the resultant graph is connected. An illustrativeexample is a network of Lorenz systems where some of thenodes are coupled through the x-variable, some through they-variable, and some through both. Proving synchroniza-tion in networks with disconnected components is a non-trivial problem as the methods based on the calculation ofthe eigenvalues of the connectivity matrix, including theMaster Stability function, seem incapable of handling thiscase in general. We extend the connection graph methodto derive bounds on the synchronization threshold in suchnetworks and show how the structure of the subgraphs andthe resultant network affects synchronization.
Igor BelykhDepartment of Mathematics and StatisticsGeorgia State [email protected]
MS54
Building a Cancer-type Specific Metabolic Net-work Model
Computational approaches to model metabolism have fo-cused on generic properties of cancer cells or tissue specificcharacteristics of normal cells. Here, we built a computa-tional model to account for cancer-type specific metabolismusing gene expression and metabolic network reconstruc-tion, thus accounting for the global dynamical effect of net-work modifications. The potential of this model to accountfor cancer-type specific post-transcriptional regulation andcharacterize normal and disease states will be discussed indetail.
Joo Sang LeeNorthwestern [email protected]
John MarkoNorthwestern UniversityMolecular [email protected]
Adilson E. MotterNorthwestern [email protected]
MS54
Controlling Nonlinear Dynamics in Complex Net-works
We have recently shown that perturbed or malfunctioningbiological and ecological networks can be rescued and con-trolled by manipulating the local network structure and/or
dynamics. Predictions go as far as to assert that certaingene deletions can rescue otherwise nonviable mutant cellsand that population control can prevent large extinctioncascades. In this talk, I will discuss how the theory of dy-namical systems can be combined with network modelingto develop computational methods to systematically con-trol the dynamics of a large range of complex networks.
Adilson E. MotterNorthwestern [email protected]
MS54
Synchronization and Network Directionality
Despite the extensive literature on the role of the networkstructure in synchronization of coupled oscillators, veryfew network parameters are shown to have simple clearrelationship with the synchronization dynamics. Here wepropose that directionality measures are good candidates:the more directional the network, the easier to synchro-nize. We show that increasing reciprocity (local direction-ality) tends to stabilize synchronous states, while addingfeedback loops against global directional structure tends todestabilize synchronization.
Takashi NishikawaClarkson [email protected]
MS55
A Novel Phase Model of Subthalamic NeuronsCapturing the Interaction Between Synaptic Ex-citation and Spike Threshold
The response of subthalamic cells to cortical input is welldescribed by a type I phase response curve (PRC). How-ever, large EPSPs delivered at late phases lower spikethreshold, shifting phase more than would be predictedfrom the infinitesimal PRC. We can capture this effect ina phase model by treating each subthalamic cell as a pairof coupled oscillators. These double-oscillators models ex-hibit behavior that is qualitatively different from single-oscillator type I cells.
Michael FarriesDepartment of BiologyUniversity of Texas at San [email protected]
Charles WilsonUniversity of Texas, San [email protected]
MS55
Firing Pattern of Mid-brain Dopaminergic Neurons
Mid-brain dopaminergic (DA) neurons display two func-tionally distinct modes of electrical activity: low- andhigh-frequency firing. The high-frequency firing is linkedto important behavioral events. However, it cannot beelicited in vitro by standard manipulations in vitro. Atwo-compartmental model of the DA cell that unites dataon firing frequencies under different experimental condi-tions has been suggested. We analyzed dynamics of thismodel. The model reproduces the separation of maximalfrequencies under NMDA synaptic stimulation vs. other
DS11 Abstracts 165
treatments.
Joon HaLBM/NIDDK/[email protected]
Alexey KuznetsovIndiana University-Purdue University [email protected]
MS55
Intermittent Synchronization of Basal Ganglia Ac-tivity
Synchronized oscillations in the beta frequency band areassociated with the motor symptoms of Parkinsons disease.In this talk I will present the results of our time-series anal-ysis of the temporal patterns of synchrony in experimen-tally recorded data. I will also consider network models,which generate similar synchronous patterns of activity andwill discuss the origin of this synchronous activity.
Leonid Rubchinsky, Choongseok ParkDepartment of Mathematical SciencesIndiana University Purdue University [email protected], [email protected]
Robert WorthDepartment of NeurosurgeryIndiana University School of [email protected]
MS55
Entrainment of a Thalamocortical Neuron to Peri-odic Sensorimotor Signals
We study a 3D conductance-based model of a single tha-lamocortical (TC) neuron in response to sensorimotor sig-nals. In particular, we focus on the entrainment of thesystem to periodic signals that alternate between ‘on’ and‘off’ states lasting for time T1 and T2, respectively. By ex-ploiting invariant sets of the system and their associatedinvariant fiber bundles that foliate the phase space, we re-duce the 3D Poincare map to the composition of two 2Dmaps, based on which we analyze the bifurcations of theentrained periodic solutions as the parameters T1 and T2
vary.
Dennis Guang YangDepartment of Mathematics, Cornell [email protected]
Yixin GuoDrexel UniversityDepartment of [email protected]
MS56
Mathematical Modelling of Adult GnRH Neuronsin the Mouse Brain
GnRH neurons are hypothalamic neurons that secretegonadotropin-releasing hormone (GnRH). We are inter-ested in understanding the mechanisms underlying the syn-chronization of calcium oscillations in GnRH neurons, howsuch oscillations are related to the membrane potential. Wehave built up a mathematical model, which can reproduceall the crucial experiments successfully. Most importantly,
one of the model predictions has been confirmed by ourcollaborator and helped them find a new channel in GnRHneurons.
Wen DuanUniversity of [email protected]
Kiho Lee, Allan HerbisonDepartment of Physiology, School of Medical ScienceUniversity of Otago, New [email protected],[email protected]
James SneydUniversity of [email protected]
MS56
Mathematical Modeling of P2X7 Receptor/channelGating
P2X7 receptor is a trimeric channel with three binding sitesfor ATP. The gating pattern of these channels can be ac-counted for by a Markov state model. This includes neg-ative cooperativity of ATP binding to unsensitized recep-tors (caused by the occupancy of one or two binding sites),channel pore opening to a low conductance state when twosites are bound, and sensitization with pore dilation to ahigh conductance state when three sites are occupied.
Anmar KhadraLaboratory of Biological ModelingNIDDK, [email protected]
Arthur ShermanNIDDK, [email protected]
Yan Zonghe, Stanko [email protected]¿, [email protected]
MS56
Model Calibration and Testing on the Same Cell
Mathematical modeling of specific cell types is often theresult of a patchwork of experimental results. Usually thismeans modeling an average cell hoping that is a faithfulrepresentation of the population. However, pituitary cellsare very heterogeneous. Here we propose a new approachthat uses the computational capabilities of programmableGraphics Processing Unit to calibrate a model and test itspredictions using the same cell
Maurizio TomaiuoloDepartment of Biological ScienceFlorida State [email protected]
Richard BertramDepartment of MathematicsFlorida State [email protected]
Arturo Gonzalez-IglesiasDepartment of Biological Science
166 DS11 Abstracts
Florida State [email protected]
Joel TabakDept of Biological SciencesFlorida State [email protected]
MS56
Searching for the Glucocorticoid Pulse Generator
A good example of pulsatile hormone secretion is the ultra-dian rhythm of glucocorticoids released from the adrenalglands. The origin of this rhythm is not known, but hasalways been assumed to be a hypothalamic neural pace-maker. In this talk I will discuss an ongoing project (mod-eling and experiment), the results of which suggest thatpulsatile glucocorticoid secretion does not originate withinthe brain at all, but emerges from a highly dynamic pe-ripheral network.
Jamie WalkerDepartment of Engineering MathematicsUniversity of [email protected]
MS57
Accelerating and Oscillating Fronts in a Three-component System
By means of a center manifold type reduction we derivean ODE system describing the evolution of front solutionsin a three-component reaction-diffusion system. These re-sults shed light on numerically observed accelerations andoscillations and pave the way for the analysis of front inter-actions in a parameter regime where the essential spectrumof a single front approaches the imaginary axis asymptoti-cally.
Martina Chirilus-BrucknerBoston [email protected]
Jens RademacherCWI, Amsterdam, [email protected]
Arjen DoelmanUniversity of [email protected]
MS57
Pattern Selection Through Invasion in Cahn-Hilliard and Phase-Field Models
We discuss spinodal decomposition initiated by localizeddisturbances from a uniform state in Cahn-Hilliard andphase-field models. Typically, disturbances grow in theform of invasion fronts that create a pattern. We analyzethe existence of such invasion fronts, in particular in re-gard to the selected wavenumber in the wake of the front.It turns out that the patterns selected in this fashion arevery different from patterns selected from random initialconditions via the fastest-linear-mode principle. In partic-ular, phase-field fronts select finite wavenumbers even inthe limit of vanishing interfacial energy, while temporal se-lection predicts infinitely small scales. We also commenton coarsening processes, spatial resonances, and period-
doubling sequences.
Arnd ScheelUniversity of MinnesotaSchool of [email protected]
MS57
Existence of Homoclinic Solutions of the Function-alized Cahn-Hilliard Equation
The functionalized Cahn-Hilliard energy models networkformation in polymer-solvent mixtures. It is given by
F(u) =
∫Ω
1
2(ε2Δu − W ′(u))2 − η
(ε2
2|∇u|2 + W (u)
)dx,
whereW (s) is a double-well potential with equal wells atu = ±b satisfying μ± ≡ W ′′(b±) > 0. For the symmetricdouble well potential, we show the variational derivativesupport a homoclinic solution by employing a contractionmapping argument. We show convergence for initial datanear the homoclinic of a perturbed second order system,removing the degeneracy in the interation via a detuningparameter.
Li Yang, Keith PromislowMichigan State [email protected], [email protected]
MS57
Towards Traveling Spots in a Three-componentFitzHugh-Nagumo System
In this presentation, we try to find traveling spot solutionsin a certain three-component FitzHugh-Nagumo system.First, we establish the existence and (non radial) stabil-ity of radially symmetric stationary spot solutions. Afterwhich, we destabilize this solution by increasing our bifur-cation parameters. We encounter a competition betweena radially symmetric Hopf bifurcation (breather) and anasymmetric drift bifurcation (traveling spot). We will fur-ther analyze this competition to abtain traveling spot so-lutions.
Peter van HeijsterDivision of Applied MathematicsBrown University, Providence [email protected]
Bjorn SandstedeBrown Universitybjorn [email protected]
MS58
Two-dimensional Attractors of the Border Colli-sion Normal Form
I will describe methods which prove the existence of acountable set of parameters for which the border colli-sion normal form has attractors with topological dimensiontwo. Periodic orbits are dense on these attractors and thedynamics is transitive (this is joint work with Chi HongWong). I will also show how classic results due to L-SYoung can be used to prove the existence of invariant mea-sures at other parameter values of the map.
Paul GlendinningUniversity of Manchester
DS11 Abstracts 167
MS58
Piecewise Isometries
Abstract not available at time of publication.
Arek GoetzMathematics DepartmentSan Francisco State [email protected]
MS58
Entropy of the Lozi Maps
The Lozi maps La,b(x, y) = (1 − a|x| + by, x) form a two-parameter family of piecewise affine homeomorphisms ofthe plane, and it presents several interesting dynamicalphenomena. The topological entropy is one of the mostwell-known invariants which measures the complexity of adynamical system. In my talk I will show how to computethe topological entropy of a Lozi map and how it behavesas a function of the parameter (a, b).
Yutaka IshiiDepartment of MathematicsKyushu University, [email protected]
MS58
Resonance in Piecewise-smooth Continuous Maps
Synchronization or mode-locking plays an important role inmany physical systems. Mode-locking regions of piecewise-smooth, continuous maps naturally display a curioussausage-like chain structure. In this talk I will demonstratehow this structure arises from a generic border-collision bi-furcation and the manner by which the structure becomessmooth as the mode-locked solution moves away from thediscontinuity.
David J. SimpsonDepartment of MathematicsUniversity of British [email protected]
MS59
Molecular Motors and Pattern Formation with Mi-crotubules
Microtubules are long cylindrical structures while kinesin isa molecular motor that walks on microtubules, using ATPas an energy source. We model the fine details of the actionof kinesin, clarifying mechanisms needed for processivity.We also model and simulate pattern formation in familiesof microtubules under the action of kinesin.
Peter BatesMichigan State UniversityDepartment of [email protected]
MS59
Multiscale Modeling for Stochastic Forest Dynam-ics
Individual-based models are widely employed to represent
and simulate complex systems. Those descriptions how-ever come with a high computational cost and perhaps un-necessary degrees of detail. In this work, we start with aspatially explicit representation of the interacting agentsand attempt to explain the systems dynamics at multiplescales by means of stochastic coarse-graining steps. We ap-ply our technique to a forest model subjected to differentdisturbance regimes.
Maud ComboulUniversity of Southern [email protected]
Roger GhanemUniversity of Southern CaliforniaAerospace and Mechanical Engineering and [email protected]
MS59
A Backward-forward Method for SimulatingStochastic Inertial Manifolds
We construct stochastic inertial manifolds numerically forstochastic differential equations with multiplicative noises.After splitting the stochastic differential equations intoa backward part and a forward part, we use the the-ory of solving backward stochastic differential equationsto achieve our goal.
Xingye Kan, Jinqiao DuanIllinois Institute of [email protected], [email protected]
Yannis KevrekidisDept. of Chemical EngineeringPrinceton [email protected]
Anthony J. RobertsUniversity of [email protected]
MS59
Dynamical Systems Driven by Levy Motions
Mean exit time for dynamical systems driven by non-Gaussian Levy noises of small intensity is considered. Thefirst exit time of solution orbits from a bounded neigh-borhood of an attracting equilibrium state is studied. Fora class of non-Gaussian Levy processes depending on thespace point with tails heavier or slower than certain α-stable levy noise, the asymptotic estimate for the meanexit time is obtained.
Zhihui YangUniversity of [email protected]
Jinqiao DuanIllinois Institute of [email protected]
Peter ImkellerInstitut fur MathematikHumboldt Universitat zu [email protected]
168 DS11 Abstracts
Ilya PavlyukevichInstitut f”ur StochastikFriedrich–Schiller–Universit”at Jena, [email protected]
MS60
Probabilistic Averages of Jacobi Operators
I will discuss my recent work on ”probabilistic averages”of Jacobi operators. These essentially tell you what infor-mation about the operator is preserved under taking trans-lates, and not looking at a single limit-point, but looking atall at the same time. In particular, my results imply char-acterization of operators whose Lyapunov exponent van-ishes on a set consisting of finitely many intervals.
Helge KruegerCalifornia Institute of [email protected]
MS60
Koopman Operator, Time Averages and the BigOil Spill
Functions that are time averages along trajectories (La-grangian time averages in fluid mechanics) of observableson the state space form the eigenspace of the Koopmanoperator at eigenvalue 1. These also form the completeset of (possibly non-smooth) invariants of a dynamical sys-tem. I will discuss how a dynamical system approaches (i.e.projects any observable onto) that set of invariants. I willalso discuss the use of the Koopman operator formalism infinite-time dynamics and describe a recent application ofthese ideas to predicting time evolution of oil flowing fromthe Deepwater Horizon Well in the Gulf of Mexico thathappened in May-August of 2010.
Igor MezicUniversity of California, Santa [email protected]
MS60
Understanding the Interplay Between LagrangianCoherent Structures, Trajectory Complexities, andTransport in the Ocean
We introduce a family of methods which allow for iden-tification of Lagrangian coherent structures in aperiodicflows that are measured over finite time intervals. Thenew methods are based on measures of complexity of fluidparticle trajectories. Basic principles of the new methodsare established, the interplay between different complexitymeasures, Lagrangian coherent structures and transport inthe ocean is investigated, and the new methods are suc-cessfully applied to realistic oceanic flows.
Irina RypinaWoods Hole Oceanographic [email protected]
Sherry ScottMarquette [email protected]
Lawrence PrattWoods Hole Oceanographic Institution
MS60
A Theory of Ergodic Partition in Continuous-timeDynamical Systems with Applications to PowerSystem Analysis
We extend the theory of ergodic partition of phase spacein discrete-time dynamical systems to continuous-time dy-namical systems with a smooth invariant measure. Thismakes it possible to identify invariant sets for measure-preserving flows such as Hamiltonian flows. Also we discussan application of the theory of ergodic partition to analy-sis and design of electric power systems with emphasis onfuture smart management.
Yoshihiko SusukiKyoto UniversityDepartment of Electrical [email protected]
MS61
Bone Remodeling Dynamics in Myeloma Bone Dis-ease
Mathematical models are developed for the dysregulatedbone remodeling that occurs in myeloma bone disease. Themodels examine the critical signaling between osteoclasts(bone resorption) and osteoblasts (bone formation). Theinteractions of osteoclasts and osteoblasts are modeled as asystem of differential equations for these cell populations.
Bruce P. AyatiUniversity of IowaDepartment of [email protected]
Claire EdwardsCancer BiologyVanderbilt University Medical [email protected]
Glenn F. WebbMathematics Department, Vanderbilt [email protected]
John P. WikswoVanderbilt UniversityVanderbilt Institute for Integrative Biosys Res and [email protected]
MS61
Spatial Dynamics in a Dengue Epidemic Model
Dengue is a tropical fever transmitted between humansthrough the bites of female mosquitos (Aedes aegypti).These bites are observed to occur mainly in the daytime.Here, we use a system of periodic difference equations tostudy the dynamics of an epidemic in which hosts havedaytime, but not nighttime, mobility and vectors have nomobility. The habitat consists of two patches and each dayis divided into four parts: evening, dawn, daytime, anddusk.
Andrew NevaiDepartment of MathematicsUniversity of Central Florida
DS11 Abstracts 169
Edy SoewonoDepartment of MathematicsInstitut Teknologi [email protected]
MS61
Stability Analysis of a Reaction-Diffusion SystemModeling Atherogenesis
A principal component of the disease process of atheroscle-rosis involves the accumulation and oxidation of low den-sity lipoproteins within the arterial wall and its corrup-tive effect on the immune process. We present a reaction-diffusion model involving chemo-taxis and perform a gen-eral stability analysis accounting for immune cell sub-species interactions, differing roles of immune cells withrespect to the components of an emerging lesion, the ef-fects of anti-oxidants, and boundary transport.
Laura RitterSouthern Polytechnic State [email protected]
Jay R. WaltonDepartment of MathematicsTexas A&[email protected]
Akif IbragimovDepartment of Mathematics and Statistics.Texas Tech [email protected]
Catherine McNealDiv, of Endocrinology, Dept. of PediatricsScott & White Hospital, Temple [email protected]
MS61
Traveling Waves of Bacterial Population Chemo-taxis
The first mathematical model describing the bacteriachemotaxis was proposed by Keller and Segel on 1971.As a cornerstone of chemotaxis modeling, the Keller-Segelmodel has attracted most extensive and persistent atten-tions in the past four decades. To simplify the analysis,most studies of traveling wave problems made a strong andunrealistic assumption that the chemical signal is not dif-fusible. In this talk, I will report some new results of thetraveling wave of the Keller-Segel model in which the chem-ical diffusion is taken into account. Particularly I will showthe zero diffusion limits of traveling wave speed and solu-tions and conclude that the chemical diffusion is negligibleonly if it is small.
Zhi-An WangDepartment of Applied MathematicsHong Kong Polytechnic [email protected]
MS62
Dynamics Induced by Bottleneck
We study the Bando car-following model on a circle in-troducing a bottleneck. Using analytical and numerical
bifurcation techniques we encounter very interesting traf-fic dynamics. There are traveling and standing waves andcombinations of both. Also so called Pony-on-a-merry-go-round solutions can be observed.
Ingenuin GasserUniversity of HamburgDepartment of [email protected]
Bodo WernerUniversity of [email protected]
MS62
Macroscopic Relations of Urban Traffic Variables:Instability, Bifurcations, and Hysteresis
Recent work has shown that the average speed and flowwithin a traffic network is related by a reproducible curve(called the Macroscopic Fundamental Diagram or MFD) iftraffic on the network is homogenously distributed. Thispresentation shows that traffic naturally tends away fromhomogeneous distributions when the network is congested.This results in bifurcations and hysteresis in the MFD.
Vikash GayahCivil EngineeringUniversity of California, [email protected]
Carlos DaganzoCivil EngineeringUniversity of [email protected]
MS62
Traffic Jams: Dynamics and Control
In this talk we review the most common modeling ap-proaches used in the vehicular traffic community andpresent the state-of-the-art methods that may be appliedto classify the dynamical behavior of these models. We willshow that using sophisticated techniques form dynamicalsystems theory may allow one to characterize the dynam-ical phenomena behind traffic jam formation. Stable andunstable motions will be described that may give the skele-ton of traffic dynamics.
Gabor OroszUniversity of Michigan, Ann ArborDepartment of Mechanical [email protected]
MS62
Absolute and Convective Instability in Traffic FlowModels
The nucleation of stop-and-go phenomena in traffic is cap-tured by linear and nonlinear instabilities in dynamical sys-tems models of driver behaviour. Data suggests that suchspatio-temporal patterns are always convected upstreamrelative to the road, however this is not always the case inmodels. We describe two methods using group and signalvelocities to distinguish between convective and absoluteinstability in a large class of microscopic traffic models.
Jonathan A. Ward
170 DS11 Abstracts
University of [email protected]
R. Eddie WilsonUniversity of Southamptonr.e.soton.ac.uk
MS63
Self-organized Criticality on Adaptive Networks
Adaptive networks are found in natural and technologicalnetworks, from neural and ecological networks, to socialnetworks or the world wide web. Mathematical models inthe spirit of statistical physics study the interplay of fastdynamical processes on a network and adaptation of thenetwork topology on a slower time scale. A particularlyinteresting case are critical phenomena on the network andtheir possible interplay with adaptive processes. In thistalk I will give an overview of adaptive network modelsthat exhibit self-organized criticality and discuss possibleapplications.
Stefan BornholdtUniversity of [email protected]
MS63
Computational Approaches to Adaptive NetworkModeling
I will present a generalized framework based on graphrewriting systems for modeling state-topology coevolutionof complex adaptive networks. I will also propose com-putational methods for automatic discovery of dynamicalrules that best capture both state transition and topolog-ical transformation in empirical data. Network evolutionis formulated in two parts: extraction and replacement ofsubnetworks. The effectiveness of the proposed frameworkand algorithms will be demonstrated through computa-tional experiments and real-world network data analysis.
Hiroki SayamaDepartments of Bioengineering & Systems Science andIndustriBinghamton [email protected]
MS63
Dynamics of Epidemic Extinction in Adaptive So-cial Networks
We study epidemic extinction in adaptive social networkswith avoidance behavior. We have shown that vaccinationof susceptible individuals in conjunction with adaptationgreatly reduces the epidemic lifetime. In the context of amean field model describing the node and link dynamics,we analyze the most probable path to extinction using largefluctuation theory. Predicted paths and extinction ratesare compared with those observed in simulations of theadaptive network system.
Leah ShawCollege of William and MaryDept. of Applied [email protected]
Ira SchwartzNaval Research Laboratory
MS63
Adaptive-network Models for Collective Motion
We propose a simple adaptive-network model describingrecent swarming experiments. Instead of tracking the spa-tial configuration of the swarm, we consider the dynamicsof the interaction network among individuals as a stochas-tic process. The model reproduces several characteristicfeatures of swarms, such as spontaneous symmetry break-ing, noise- and density-driven order-disorder transitions,and intermittency. Complementing the usual agent-basedmodels, it unveils the essential elements required to recoverthe observed swarming behavior.
Cristian HuepeUnaffiliated NSF [email protected]
Gerd ZschalerMax-Planck-Institut fur Physik komplexer [email protected]
Anne-Ly DoMax Planck Institute for the Physics of Complex [email protected]
Thilo GrossMPI for the Physics of Complex [email protected]
MS64
Multidimensional Stability of Planar Fronts in theDiscrete Allen-Cahn Equation
We establish multidimensional stability in �1 of bistableplanar fronts for the Allen-Cahn equation on Z2. Theproof makes use of comparison principles and sub-/super-solution pairs. The relevant sub-/super-solutions areadapted from recent work of Matano, Nara and Taniguchion the Allen-Cahn equation in Rn. The chief difficulty inpassing to the spatially discrete setting is the anisotropy ofthe discrete laplacian.
Aaron HoffmanBoston UniversityDepartment of Mathematics and [email protected]
Erik Van VleckDepartment of MathematicsUniversity of [email protected]
MS64
The Transverse Instability of Periodic TravelingWaves in the Generalized Kadomtsev-Petviashvili(KP) Equation
We consider the spectral instability of periodic travelingwave solutions of the gKdV equation to transverse pertur-bations in the gKP equation. By analyzing high and lowfrequency limits of the appropriate periodic Evans func-tion, we derive an orientation index which yields sufficientconditions for such an instability to occur. This index isgeometric in nature and applies to arbitrary periodic trav-eling waves with minor smoothness and convexity assump-
DS11 Abstracts 171
tions on the nonlinearity. Using the integrable structure ofthe ordinary differential equation governing the travelingwave profiles, we are then able to calculate the resultingorientation index for the elliptic function solutions of theKorteweg-de Vries and modified Korteweg-de Vries equa-tions. This is joint work with Kevin Zumbrun.
Mat JohnsonIndiana [email protected]
MS64
Asymptotic Stability of Small Gap Solitons in theNonlinear Dirac Equations
We prove dispersive decay estimates for the one-dimensional Dirac operator and use them to prove asymp-totic stability of small gap solitons in the nonlinear Diracequations with quintic and higher-order nonlinear terms.
Atanas StefanovUniversity of [email protected]
MS64
Phase Transition Waves in a Diatomic Chain
We consider Hamiltonian dynamics of a chain of two al-ternating masses connected by phase-transforming springswith nonconvex elastic energy. Assuming bilinear inter-actions, we construct explicit traveling wave solutions foreven and odd strains representing a phase transition wavepropagating through the chain and numerically investigatetheir stability. We show that the ratio of the two massessubstantially affects existence, stability and various prop-erties of such solutions.
Anna VainchteinDepartment of MathematicsUniversity of [email protected]
Panayotis KevrekidisUniversity of [email protected]
MS65
Non-synchronous Behavior of Oscillators onGraphs
In this talk, I will discuss the dynamics of oscillators oncertain graphs where each node has the same number ofedges. The problem arises from the study of networks ofdiscrete oscillators on the surface of the sphere where thereis local interaction. Such systems are found in the flagel-lar system of the Volvox, calcium dynamics on the surfaceof an oocyte, and abstractly in surface EEG recordings.We start with a dodecahedral graph and prove that thereare stable rotating wave solutions coexisting with stablesynchronous solutions. We extend the results of the do-decahedral system to a class of graphs that include the do-decahedron. We also study bifurcations of these rotatingwaves as coupling strength and a dispersion term change.The work is joint with Mr. Lawrence Udeigwe.
Bard ErmentroutUniversity of PittsburghDepartment of Mathematics
MS65
Collective Phase Diffusion in Networks of NoisyOscillators
Examples of collective dynamics stemming from interac-tions among noisy individual components include heart-beats and circadian rhythms. Because each componentis noisy, collective dynamics involve fluctuations. Never-theless, the relation between the fluctuations in individualcomponents and those in collective dynamics remains elu-sive. We present our recent theoretical work on this sub-ject. We analytically show that the structure of networksdetermines the intensity of fluctuations in the collectivedynamics. We also show some examples.
Naoki MasudaThe University of TokyoGraduate School of Information Science and [email protected]
Yoji KawamuraThe Earth Simulator CenterJapan Agency for Marine-Earth Science and [email protected]
Hiroshi KoriDivision of Advanced SciencesOchanomizu [email protected]
MS65
The Impact of Cellular Dynamics, Synaptic Noise,and Synaptic Convergence on Correlations andSynchrony
We explore several fundamental mechanisms that deter-mine how correlations and synchrony propagate in net-works of neurons. We show that single-cell dynamics andsynaptic variability significantly reduce correlations frominput to output, but that synaptic convergence dramati-cally amplifies correlations downstream. Perhaps surpris-ingly, we find that synaptic convergence is the primarymechanism responsible for the synchronization of feedfor-ward chains, and that synaptic divergence plays a compar-atively minor role.
Robert RosenbaumUniversity of HoustonDept. of [email protected]
MS65
The Interaction of Intrinsic Dynamics and Net-work Topology in Determining Network Burst Syn-chrony
Respiratory brainstem networks generate synchronizedbursting despite heterogeneity in neuronal components dy-namics. The networks connection topology features denseclusters with occasional connections between clusters. Us-ing computational models, we compare characteristics ofnetwork bursting with bursting arising in small-world,scale-free, random, and regular networks constructed withidentical neuronal components. We characterize how mea-sures of burst synchronization are determined by interac-tions of network topology with neuronal dynamics (qui-
172 DS11 Abstracts
escent/bursting/tonic) at central network positions andsynaptic strengths between neurons.
Jonathan E. RubinUniversity of PittsburghDepartment of [email protected]
MS66
Modeling Particle Suspensions Near Ciliated Sur-faces
Using computer simulations, we examine how biomimeticcilia can be utilized to control the motion of microscopicparticles suspended in a viscous fluid. The cilia are mod-eled as deformable, elastic filaments and the simulationscapture the complex fluid-structure interactions amongthese filaments, suspended particles, channel walls and sur-rounding solution. We show that biomimetic cilia can bearranged to create hydrodynamic currents that can eitherdirect particles towards the ciliated surface or expel themaway, thereby modifying the effective interactions betweensolid surfaces and particulates. The findings uncover a newroute for controlling the deposition of microscopic particlesin microfluidic devices.
Alexander AlexeevGeorge W. Woodruff School of Mechanical EngineeringGeorgia Institute of [email protected]
MS66
Inertial Focusing, Ordering, and Separation of Par-ticles in Confined Flows
Fluid inertia is usually not considered in microfluidic flowsbut has recently been shown to be of great practical usefor continuous manipulation of particles and cells. I willdemonstrate several unique phenomena that allow for sort-ing and focusing of cells and particles in three dimensionsunder continuous flow. I will briefly discuss inertial mi-gration theory and our recent results, demonstrating con-trolled creation of ordered particle lattices, and suggestinga critical role of interparticle hydrodynamic interactionsinduced by confinement. Engineered inertially focusedstreams of cells and particles are poised to provide next-generation filter-less filters and simplified high-throughputcytometry instruments which ultimately may aid in cost-effective medical diagnostics, water treatment, and indus-trial filtration and waste minimization.
Dino Di CarloDepartment of BioengineeringUniversity of California Los [email protected]
MS66
Manipulation of Suspended Micro-Particles via Lo-calized Fluid Boundary Dynamics
This talk will address the idealized modeling, high-fidelitysimulation, and laboratory realization of systems for ma-nipulating particles suspended in fluids using laterally os-cillating cylindrical filaments at low Reynolds number. Theidealized problem will be framed in the context of geo-metric mechanics and nonlinear control. Numerical stud-ies of planar particle transport near oscillating cylinders,based on a viscous vortex particle method, will be pre-sented alongside preliminary experimental data depicting
the motion of neutrally buoyant particles in proximity tofibers of micron-scale thickness exhibiting resonant vibra-tions in water.
Scott D. KellyMechanical Engineering and Engineering ScienceUniversity of North Carolina at [email protected]
MS66
Interaction Between an Elastic Filament and theVesicle Membrane
The primary cilium is found for all non-dividing mam-malian cells. Since its discover a century ago, only recentlyhas more understanding of the biological role of primarycilia been gained. In this work slender-body formulationis utilized to describe the dynamics of the primary cilium,modeled as an elastic filament attached to a solid wall ormembrane. Comparison with the experimental data will beprovided. Coupling between the filament/membrane sys-tem and the mechanosensitive channel (MscL) show howthe primary cilium functions as a probe of the extracellularflow.
Yuan-Nan YoungDepartment of Mathematical [email protected]
MS67
Dynamics of Plateau Bursting in Dependence onthe Location of its Equilibrium
The transition from tonic spiking to plateau bursting and,in particular, pseudo-plateau bursting is still not well un-derstood. We investigate the influence of the location ofthe system’s equilibrium using a generic polynomial modelof Hindmarsh-Rose type. We relate our global numericalexplorations to local results known from singular pertur-bation theory and argue the existence of a connected (hy-per)surface of periodic orbits in two-parameter space thatcontains both tonic spiking and plateau bursting solutions.
Hinke M. OsingaUniversity of BristolDepartment of Engineering [email protected]
Krasimira Tsaneva-AtanasovaDepartment of Engineering MathematicsUniversity of [email protected]
MS67
From Plateau to Pseudo-Plateau Bursting: Makingthe Transition
Plateau and pseudo-plateau bursting are observed in neu-rons and endocrine cells, respectively, and have differentproperties and likely serve different functions. We showthat a model for one type of cell produces bursting of thetype seen in the other type without large changes to themodel. We provide a procedure for achieving this transi-tion. This suggests that the design principles for burstingin endocrine cells are quantitative variations of those forbursting in neurons.
Wondimu W. Teka
DS11 Abstracts 173
Department of MathematicsFlorida State [email protected]
Krasimira Tsaneva-AtanasovaDepartment of Engineering MathematicsUniversity of [email protected]
Richard BertramDepartment of MathematicsFlorida State [email protected]
Joel TabakDept of Biological SciencesFlorida State [email protected]
MS67
Decoding Pulsatile GnRH Signals
We present a signalling pathway model of GnRH-dependent transcriptional activation developed to dissectthe dynamic mechanisms of differential regulation of go-nadotropin subunit genes. The model incorporates key sig-nalling molecules, including extracellular-signal regulatedkinase (ERK) and calcium-dependent activation of NuclearFactor of Activated T-Cells (NFAT), as well as transloca-tion of activated/inactivated ERK and NFAT across thenuclear envelope. We show that simulations with varyingin dose and frequency GnRH pulsatile inputs agree verywell with experimental measurements of GnRH-dependentERK and NFAT responses. Furthermore in silico experi-ments designed to probe trancriptional effects downstreamof ERK and NFAT reveal that interaction between tran-scription factors is sufficient to account for frequency dis-crimination.
Krasimira Tsaneva-AtanasovaDepartment of Engineering MathematicsUniversity of [email protected]
Craig McArdleLaboratories for Integrative Neuroscience andEndocrinology,University of [email protected]
MS67
Model-based Study of the Back-and-forth Transi-tions Between the Pulsatile and Surge Phase inGnRH Secretion
The secretion of Gonadotropin Releasing Hormone(GnRH) by specific hypothalamic neurons plays a majorrole in the neuroendocrine control of the reproductive func-tion in female mammals. The periodic back-and-forth tran-sitions between the pulsatile secretion phase and the pre-ovulatory surge are among the most crucial mechanismsunderlying this control, but they remain misunderstood onthe biological level. Using a mean field model, I will ana-lyze the dynamical properties that enable one to generatethese mechanisms.
Alexandre VidalUniversity of Evry-Val-d’Essonne
Department of Mathematics - Analysis and [email protected]
Martin KrupaINRIA Paris-Rocquencourt Research Centre(Invited Professor)[email protected]
Frederique ClementINRIA [email protected]
Mathieu DesrochesUniversity of BristolEngineering [email protected]
MS68
Simplifying the Complexity of Pipe Flow
When fluid flows through a pipe, channel, or duct, thereare two basic forms of motion: smooth laminar motionand complex turbulent motion. The discontinuous transi-tion between these states is a fundamental problem thathas been studied for more than 125 years. I will recallsome of the history of hydrodynamic stability theory witha view to explaining why even the simplest case, pipe flow,is both a fascinating and difficult problem. I will then ex-plain recent developments that have led to remarkable newinsights and shown a deep connection between the transi-tion to turbulence and non-equilibrium phase transitionssuch as directed percolation.
Dwight BarkleyUniversity of WarwickMathematics [email protected]
MS68
Stochastic Effects in a Two-component SignallingSystem
Two-component signalling systems (TCS) are frequentlyused by bacteria to adapt to changing environmental sig-nals, and are implicated, for example, in the transitionbetween rapid growth and dormancy in Mycobacterium tu-berculosis. We compare deterministic and stochastic ap-proaches, including equation-free methods, to the analy-sis of a TCS, seeking to understand the relationship be-tween autoregulation of the response regulator gene and‘all-or-none’, graded and mixed-mode stochastic switchingresponses.
Rebecca B. HoyleUniversity of SurreyDepartment of [email protected]
Andrzej KierzekUniversity of SurreyDivision of Microbial [email protected]
MS68
A Reduced Model for Binocular Rivalry
Binocular rivalry occurs when two very different images
174 DS11 Abstracts
are presented to the two eyes. Previous models for thisphenomenon have been either phenomenological rate mod-els or more realistic spiking neuron models. Few attemptshave been made to derive the former type of model fromthe latter. We give such a derivation, using data-miningtechniques to automatically extract appropriate variablesfor a low-dimensional description.
Carlo R. LaingMassey [email protected]
MS68
A Micro/macro Acceleration Technique for MonteCarlo Simulation of Polymeric Fluids
We present and analyze a micro/macro acceleration tech-nique for the Monte Carlo simulation of stochastic differ-ential equations (SDEs) in which there is a separation be-tween the (fast) time-scale on which individual trajectoriesof the SDE need to be simulated and the (slow) time- scaleon which we want to observe the (macroscopic) functionof interest. The method performs short bursts of micro-scopic simulation using an ensemble of SDE realizations,after which the ensemble is restricted to a number of macro-scopic state variables. The resulting macroscopic state isthen extrapolated forward in time and the ensemble is pro-jected onto the extrapolated macroscopic state. We relatethe algorithm to existing analytical and numerical closureapproximations and provide a first analysis of its conver-gence in terms of extrapolation time step and number ofmacroscopic state variables. The effects of the different ap-proximations on the resulting error are illustrated via nu-merical experiments. This talk is based on joint work withKristian Debrabant, Vincent Legat and Tony Lelievre.
Giovanni SamaeyDepartment of Computer Science, K. U. [email protected]
MS69
A Chemostat Model for Bacteria-phage Interactionwith Infinite Distributed Delay
The interaction between bacteria and bacteriophage(phage) has been an interesting topic for scientific stud-ies since 1910’s. Nevertheless, mathematical models werenot proposed until 1960’s. Levin et. al formulated a gen-eral model with Delay Differential Equations (DDEs) andcarried out a series of experiments and observations. Theclassic chemostat theory as well as laboratory experimentsconfirm that two bacteria cannot coexist in a chemostatprovided one is the superior competitor. However, accord-ing to Levin’s experiment, apparently the coexistence oftwo bacteria species is possible if a phage species, whichattacks only the superior bacteria, presents. Our goal is togive an rigorous mathematical analysis and show that thecoexistence of two bacteria under certain conditions. Inthis study, we formulated a DDE system similar to Levin’swith infinite distributed delays. By using the linear chaintrick, we reduced this system into an ODE system and an-alyzed bifurcations of equilibrium points and showed somepersistence results.
Zhun HanArizona State [email protected]
Hal L. SmithArizona state [email protected]
MS69
Modeling an Obligate Mutualism: Leaf-cutter Antsand its Fungus Garden
We propose a simple mathematical model by applyingMichaelis-Menton equations of enzyme kinetics to studythe mutualistic interaction between the leaf cutter ant andits fungus garden at the early stage of colony expansion.We derive the sufficient conditions on the extinction andcoexistence of these two species. In addition, we give aregion of initial condition that leads to the extinction oftwo species when the model has an interior attractor. Ourglobal analysis indicates that the division of labor by work-ers ants and initial conditions are two important factorsthat determine whether leaf cutter ants colonies and theirfungus garden survive and grow can exist or not. We val-idate the model by doing the comparing between modelsimulations and data on fungal and ant colony growth ratesunder laboratory conditions. We perform sensitive analy-sis and parameter estimation of the model based on theexperimental data to gain more biological insights on theecological interactions between leaf cutter ants and theirfungus garden. Finally, we give conclusions and discusspotential future work.
Yun KangApplied Sciences and Mathematics, Arizona [email protected]
Rebecca ClarkSchool of Life Sciences,Arizona State [email protected]
Michael MakiyamaIra A Fulton Engineering,Arizona State [email protected]
Jennifer FewellSchool of Life Sciences,Arizona State [email protected]
MS69
The Timing of Insect Developmental and Trajec-tory of Bark Beetle Outbreaks
Temperatures directly but nonlinearly influence the ratesat which insects complete development in their various lifestages and therefore the timing (phenology) of their emer-gence. Bark beetles, aggressive insects which attack livinghost trees with significant defensive mechanisms, exist in aprecarious niche which depends on carefully synchronizedtiming. Changing temperatures in Western North Amer-ica have broadened that niche across vastly larger regions,leading to outbreaks in conifer forests. Impacts are cur-rently larger than the impact of fire in these ecosystems.This talk outlines the development of mathematical modelsfor bark beetle phenology and how the dynamics of phe-nology influences the course and severity of outbreaks.
James PowellDepartment of Mathematics and StatisticsUtah State University
DS11 Abstracts 175
MS69
Modeling Bee Pollination of Almond Orchards withCross- and Self-diffusion: An Application of theShigesada-Kawasaki-Teramoto Model
California’s almond industry is one of America’s top agri-cultural exports worth $1.9 billion annually. Success-ful production of almonds depends on the pollinator ser-vices of primarily honeybees, although pollination by wildbees is being investigated as an alternative because of re-cent problems with honeybees. We model pollinator ser-vices of honey and wild bees, as well as their interactionsin almond orchards. Utilizing the Shigesada-Kawasaki-Teramoto model (1979) which describes the density of twospecies in a two-dimensional environment of variable favor-ableness with respect to intrinsic diffusions and interactionsof species, we model almond pollination by wild and honeybees with environmental favorableness based on empiricaldata measuring the attractiveness of the canopy for honeyand wild bees. Using the spectral-Galerkin method in arectangular domain, we numerically solved the 2D nonlin-ear parabolic PDE and examine the result of varying theparameters. Empirical data on bee distribution was com-pared with the numerical solutions. We use the model todetermine what circumstances the presence of wild, soli-tary bees can increase the dispersion of honeybees, thusincreasing pollination.
Kamuela E. Yong, Yi Li, Stephen HendrixUniversity of [email protected], [email protected],[email protected]
MS70
Global Invariant Manifolds Organizing ShilnikovChaos
It is widely known that, under certain conditions, the ex-istence of a homoclinic orbit to a saddle-focus equilibriuminduces chaotic dynamics. This is known as a Shilnikovhomoclinic bifurcation. The chaotic region near the ho-moclinc trajectory is filled by countably many periodic or-bits of saddle type. The key question is how these objectsand their corresponding higher-dimensional global invari-ant manifolds change in this bifurcation to reorganize thephase space and define the structure of Shilnikov chaos.
Pablo Aguirre, Bernd KrauskopfUniversity of BristolDepartment of Engineering [email protected], [email protected]
Hinke M. OsingaUniversity of BristolDepartment of Engineering [email protected]
MS70
Two-dimensional Global Manifolds in the Transi-tion to Chaos in the Lorenz System
This talk considers the transition from simple to chaoticdynamics in the Lorenz system as the Rayleigh parameteris increased to its classical value of 28. More specifically,we show how the two-dimensional stable manifolds of theorigin and of the primary saddle periodic orbits bifurcate
and organize the dynamics throughout the entire three-dimensional phase space.
Bernd KrauskopfUniversity of BristolDepartment of Engineering [email protected]
Hinke M. OsingaUniversity of BristolDepartment of Engineering [email protected]
Eusebius J. DoedelConcordia UniversityDepartment of Computer Science and [email protected]
MS70
Unfoldings of Singular Hopf Bifurcation
We present a systematic study of a 5-parameter normalform for singular Hopf bifurcation in vector fields with onefast and two slow variables, introduced by Guckenheimerin 2008. We compute numerically the position of a tan-gency of invariant manifolds that can mark the onset ofmixed-mode oscillations in systems with a singular Hopfbifurcation. A detailed picture of the bifurcation structureof the normal form is developed.
Philipp MeerkampCornell UniversityDepartment of [email protected]
John GuckenheimerCornell [email protected]
MS70
A Lin’s Method Approach to Finding and Continu-ing Heteroclinic Connections Between Periodic Or-bits of Saddle Type
It is known that the dynamics of many mathematical mod-els of intracellular calcium is strongly influenced by thepresence of global bifurcations, including homoclinic andheteroclinic bifurcations of periodic orbits. Using a simplecalcium model, we illustrate a numerical method, basedon Lin’s approach, for finding and continuing heteroclinicconnections between periodic orbits. Locating such bifur-cations helps to understand the overall bifurcation struc-ture of calcium dynamics. This approach can also apply toother excitable models.
Wenjun ZhangUniversity of [email protected]
Bernd KrauskopfUniversity of BristolDepartment of Engineering [email protected]
Vivien KirkUniversity of [email protected]
176 DS11 Abstracts
MS71
Spatial Modeling of Bacterial Antibiotic Tolerence
Persistent bacterial infections are a serious and growingmedical problem. Antibiotic tolerant cells, termed persis-ters, are genetically identical to those killed by antibioticsbut regrow after antibiotics are removed. Persister forma-tion has been linked to quorum sensing, the ability of bac-teria to determine their local population density, and withthe formation of biofilms, surface-growing bacterial com-munities particularly difficult to eradicate with antibiotictreatments. Extending a previous model of bacterial colonypattern formation, we present a reaction-diffusion modelof bacterial growth which includes density-dependent per-sister formation. The model also exhibits separation oftemporal and spatial scales between persister and regularbacteria. We investigate the pattern formation propertiesof the model as a number of experimentally accessible pa-rameters are varied.
John BurkeBoston [email protected]
MS71
Dynamics of Persister Formation: Dosing andFluid Interactions
Bacterial biofilms are widely acknowledged to be sourcesof recalcitrant infections and colonization in a variety ofmedical, environmental and industrial settings. This re-calcitrance is evidenced by recurrence of the infection,even after extremely long application of biocides or an-tibiotics. Explanations for this tolerance include physicalprotection of the bacteria by the surrounding extracellu-lar matrix, physiological protection arising from nutrientgradients formed by the spatial distribution of the bacteriawithin the biofilm and the existence of specialized pheno-types of bacteria that forgo reproduction in order to evadethe antimicrobial agent. This talk will focus on the analy-sis of recent models that incorporate all of these tolerancemechanisms into a model of biofilm dynamics. In partic-ular, we will focus on the affect of the external flow envi-ronment on the disinfection process. The contrast betweendynamics within free channels and partially blocked chan-nels indicates that the spatial environment plays a muchstronger role than has been previously thought.
Nick CoganDepartment of MathematicsFlorida State [email protected]
MS71
Pattern Formation in Reaction-diffusion Systemswith an External Morphogen Gradient
Gradients of signalling molecules are abundant in the earlyembryo. They are known to be central to development inmany cases, although the exact mechanism of how they in-fluence pattern formation is often still unknown. A related,but distinct concept is the Turing mechanism in reaction-diffusion systems. Since Turing showed in the 1950s howthe interplay of two or more chemicals can spontaneouslygive rise to patterns, it has become a paradigm for pat-tern formation and it has been proposed as an explana-tion for many developmental phenomena. To investigatethe possible interplay between the Turing mechanism andmorphogen gradients, we propose a generic model of a
reaction-diffusion system in the presence of a linear mor-phogen gradient. We assume that this morphogen gradientis established independently of the reaction-diffusion sys-tem. Hence it is referred to as an ”external” morphogen. Itacts by increasing the production of the activator chemicalproportional to the morphogen concentration. The modelis motivated by several existing models in developmen-tal biology in which a Turing patterning mechanism hasbeen proposed and various chemical gradients are known tobe important for development. Mathematically, this leadsto reaction-diffusion equations with explicit spatial depen-dence. We investigate how the Turing pattern is affected,if it exists. We also apply our general findings to a modelof skeletal pattern formation in vertebrate limbs and showhow they can shed light on some experimental findings con-cerning the action of the protein Sonic Hedgehog.
Tilmann GlimmWestern Washington [email protected]
MS71
Dorsal-ventral Patterning in Sea Urchin andDrosophila Embryos
The dorsal-ventral axis in Drosophila is specified by gradi-ents of bone morphogenetic proteins (BMPs). While ini-tially secreted in a broad region, later concentrate into anarrow band, designating the dorsal-most 10% of the em-bryo. Modeling papers have focused on the dynamics seenin Drosophila, but the same mechanism specifies the seaurchin axis. Yet in urchins, the BMP secretion and ex-pression domains are complementary. Reaction-diffusionmodels are considered for the patterning seen in both or-ganisms.
Heather D. HardwayBoston UniversityDepartment of Mathematics and [email protected]
MS72
Glass Networks: Overview and Recent Results
Gene regulatory networks and neural networks can bestrongly switching systems, allowing approximation bypiecewise-linear equations called Glass networks. Flow isstructured by a series of attracting (focal) points, whichmay or may not be reachable. Periodic and more complexbehavior can arise. Also, flow can be constrained temporar-ily in threshold regions far from focal points. All of thesebehaviors can by treated analytically, via discrete mapsbetween threshold hyperplanes, and sliding modes withinthem.
Roderick EdwardsUniversity of VictoriaDept. Math and [email protected]
MS72
Nonlinear Dynamics of Gene Regulatory Networks:An Automated Analyzer
This talk deals with the dynamics of gene regulatory mod-els where regulation is assumed threshold dependent anddescribed by steep sigmoids. In domains where all vari-able values are far from thresholds, the dynamics is fairlyeasy to describe. The challenge is to analyze the flow in
DS11 Abstracts 177
the narrow domains where at least one variable value isclose to one of its thresholds. Under a biologically reason-able assumption, rules that determine the system flow areestablished.
Liliana IroniIMATI - CNRPavia (Italy)[email protected]
Luigi [email protected]
Erik PlahteDep. Mathematical Sciences and Technology andCIGENENorwegian University of Life Sciences, Aaserik.plahte
Valeria SimonciniUniversita’ di Bologna, [email protected]
MS72
Transient Vector Field Effects on Oscillations in aNeuromechanical Model of Limbed Locomotion
We analyze a closed-loop locomotor model in which a cen-tral pattern generator drives a single-joint limb and receivesafferent feedback. Transitions associated with changes inground reaction force or motoneuron outputs abruptly al-ter the vector field in the limb dynamics phase plane. Thepositions of the locomotor oscillation trajectory relative tothese transient vector fields and their critical points explainthe model’s ability to replicate an experimentally observedlocomotor asymmetry. A contraction argument relying onthese transitions provides conditions for existence of a pe-riodic orbit in a reduced model.
Lucy SpardyUniversity of [email protected]
Sergey Markin, Natalia ShevtsovaDrexel University College of [email protected],[email protected]
Boris PrilutskyGeorgia Institute of [email protected]
Ilya A. RybakDrexel University College of [email protected]
Jonathan RubinUniversity of PittsburghPittsburgh, [email protected]
MS72
Phase Resetting in Phaseless Systems
Oscillatory biological behavior often suggests the presenceof a stable limit cycle, for which one may define a phase re-
setting curve in terms of the asymptotic response to smallperturbations. Empirically, rhythmic behavior also ap-pears in systems without a well defined asymptotic phase,for instance spiral sinks or heteroclinic cycles when thesesystems are perturbed by noise. We will discuss the chal-lenge of defining ”phase resetting” for systems lacking awell defined asymptotic phase.
Peter J. ThomasCase Western Reserve [email protected]
Kendrick ShawCase Western Reserve UniversityDepartment of [email protected]
Klaus StiefelOkinawa Institute of Science and [email protected]
Hillel ChielCase Western Reserve [email protected]
MS73
Robustness of Overlapping Modular Networks
Many systems can be modeled using networks of coupledoverlapping modules. Elements of these networks performindividual and collective tasks such as generating and con-suming electrical load or transmitting data. We study theirrobustness: a random fraction of the elements fail whichmay cause the network to lose global connectivity. Thesemodules can become uncoupled (non-overlapping) beforethe network falls apart. This may explain how missingdata affects the community structure of large-scale socialnetworks.
James Bagrow, Yong-Yeol AhnCenter for Complex Network ResearchNortheastern [email protected], [email protected]
Sune LehmannDTU InformaticsTechnical University of [email protected]
MS73
Gang Dynamics in Los Angeles
Gang violence is one of the major sources of aggravatedassaults and homicide Los Angeles. Therefore, it is impor-tant to understand the rivalry network among gangs andhow such a rivalry network could emerge and evolve. Wepropose an agent-based model to simulate the emergenceof a gang rivalry network. As a case study, our modelfocuses on an area of Los Angeles known as Hollenbeck.Agents’ perform a biased Levy walk and their movementsare coupled to an evolving network of gang rivalries, whichis determined by previous interactions among agents in thesystem. We integrate gang data provided by the LAPD, ge-ographic information, and behavioral dynamics suggestedby the criminology literature. The major highways, rivers,and the locations of gangs’ centers of activity influence theagents’ motion. We use common metrics from graph the-ory to analyze our model, comparing networks produced
178 DS11 Abstracts
by our simulations to the real-world network available inthe criminology literature.
Alethea BarbaroUniversity of California, Los [email protected]
MS73
Collective Chaotic Incoherence Stabilizes Synchro-nization Chimera
We introduce a new state in coupled chaotic oscillators,related to chimera states for phase oscillators. We presentmixed behavior in networks of some coherent componentsthat synchronize, coexisting with decoherence as a gener-alized chimera state. We demonstrate existence of suchmixed states together with analysis predicting the phe-nomenon that further shows the coherence is caused bythe coexisting decoherence mimicking a stochastic drive tostabilize the coherent oscillators as mechanism of self sym-metry breaking.
Erik BolltClarkson [email protected]
Sun JieNorthwestern [email protected]
Takashi NishikawaClarkson Universitytakashi [email protected]
MS73
Social Influence and the Spread of Facebook Ap-plications
Social influence drives offline and online behavior. Priorwork on the diffusion of innovations in spatial regions orsocial networks has focused on the spread of one particulartechnology among a subset of adopters. We study socialinfluence processes by tracking the popularity of a completeset of applications installed by Facebook users. We analyzethe collective behavior induced by 100 million applicationinstallations, finding that two distinct regimes of behavioremerge in the system.
Jukka-Pekka OnnelaHarvard [email protected]
MS74
Hysteretic Capillary Interactions in Models ofAtomic-Force Microscopy: a Bifurcation Paradigmfor Nonsmooth Systems
This paper collects four distinct instances of grazing con-tact of a periodic trajectory in hybrid dynamical systemsunder a common framework and establishes general prop-erties of the associated near-grazing dynamics. It is shownthat commonly used physical models of rigid or compliantmechanical contact and capillary adhesion, e.g., models oftapping-mode atomic force microscopy in the presence ofthin fluid films on the sample and the probe tip, satisfy theconditions required by the framework.
Harry Dankowicz
University of [email protected]
Michael KatzenbachDepartment of Mechanical Science and EngineeringUniversity of Illinois at [email protected]
MS74
Good Vibrations: Bimodal Atomic Force Mi-croscopy
Improving spatial resolution, data acquisition times andmaterial properties imaging are some long lasting goals ofamplitude modulation AFM. Currently, the most promis-ing approaches to reach those goals involve the excitationof several frequencies of the tips oscillation. Bimodal AFMis an emerging technique that is characterized by a highsignal-to-noise ratio and the versatility to measure differ-ent forces. The high sensitivity enables high resolutionimaging under the application of sub-100 pN peak forces.
Ricardo GarciaInstituto de Microelectronica de Madrid (CSIC)[email protected]
MS74
High Speed Atomic Force Microscopy
High speed atomic force microscopy is capable of delivering3D images of biological samples at over 1000 fps. The ba-sic principles of atomic force microscopes will be explainedfollowed by the current understanding of the microscope’sinteraction with the sample surface during the imaging pro-cess. A combination of experiments and theory are usedto explain the low friction regime between the microscopeand the sample and how this enables the high frame rateof HSAFM.
Oliver D. PaytonUniversity of Bristol, [email protected]
MS74
The Dynamics of Tapping Mode Atomic Force Mi-croscopy
In this talk I will discuss recent work that will highlight(a) the spatiotemporal dynamics of vibrating cantileversstudied by integrating a commercial AFM with a scanningDoppler vibrometer, with an insight into Proper Orthog-onal Decomposition (POD) of cantilever dynamics and itsimplications, (b) Multi-modal interactions when AFM can-tilevers are used in liquids, including energy transfer fromlower to higher modes and also subharmonic transfer ofenergy from higher to lower modes.
Arvind RamanPurdue [email protected]
MS75
Variational Approximations in Discrete NonlinearSchrodinger Equations
The variational approximation (VA) is a robust tool thatcan be used to study solitary waves in infinite dimen-
DS11 Abstracts 179
sional Hamiltonian systems, like the discrete nonlinearSchrodinger (DNLS) equation. Besides explaining the un-derlying ideas of the reduction itself, I will discuss specificresults pertaining to a DNLS equation with competing cu-bic and quintic nonlinearities in one- and two-dimensionallattices, including an accurate description of complex bi-furcation structure such as snaking.
Christopher ChongUniversitat [email protected]
MS75
Principal Component Analysis of the Ginzburg-Landau Equation
A low-dimensional description of the cubic-quinticGinzburg-Landau equation is constructed via the properorthogonal decomposition to characterize the pulse dynam-ics in a ring cavity laser mode-locked by a saturable ab-sorber. The bifurcation diagram of the reduced modelshows that the transition from a single pulse to a doublepulse configuration is via a Hopf bifurcation. The reduc-tion technique can be used as an efficient algorithm forobtaining high-energy pulses in the laser cavity withoutgoing through the multi-pulsing instability.
Edwin DingApplied MathematicsUniversity of [email protected]
Eli ShlizermanUniversity of Washington, [email protected]
J. Nathan KutzUniversity of WashingtonDept of Applied [email protected]
MS75
Dynamics and Pattern Formation in Large Sys-tems of Spatially-Coupled Oscillators with FiniteResponse Times
We study large systems of spatially-coupled oscillator net-works with heterogeneous distributions in natural fre-quency and response time delays. Using the Ott-Antonsenansatz and adopting a strategy similar to that in the re-cent work of Laing, the microscopic dynamics of these sys-tems is reduced to a macroscopic PDE description. We nu-merically find that finite response time leads to interestingspatio-temporal dynamical behaviors including propagat-ing fronts, spots, target patterns, chimerae, spiral waves,etc.
Wai S. LeeInstitute for Research in Electronics and Applied PhysicsUniversity of [email protected]
Juan G. RestrepoDepartment of Applied MathematicsUniversity of Colorado at [email protected]
Edward OttUniversity of Maryland
Inst. for Plasma [email protected]
Thomas AntonsenInstitute for Research in Electronics and Applied PhysicsUniversity of [email protected]
MS75
Parabolic Resonance Instability in Near-integrablePDEs
The parabolic resonance instability appears persistently innear integrable n d.o.f. Hamiltonian families depending onp parameters provided n+p ≥ 3. This ubiquitous finite di-mensional instability may be analyzed using the adiabaticchaos methodology. An analogous instability mechanismhas been identified in near integrable PDE equations suchas the forced periodic 1D NLS equation and the driven sur-face waves. Some of the geometric characteristics of thisinstability in the PDE context will be described.
Eli ShlizermanUniversity of Washington, [email protected]
Vered Rom-KedarThe Weizmann InstituteApplied Math & Computer [email protected]
MS76
Effective Langevin Equations for HeterogeneousCoupled Neural Networks
We construct effective Langevin equations for single neu-rons within coupled neural networks and explore the effectsof heterogeneity on the population statistics and stability.The parameters of the Langevin equation are dependentupon the properties of the other neurons within the net-work. We discuss the impact of heterogeneity on the pos-sibility of various coding schemes in the network, for ex-ample whether the neurons respect a phase-coding versusa rate-coding mechanism.
Michael BuiceLBM/NIDDKNational Institutes of [email protected]
Carson C. ChowLaboratory of Biological ModelingNIDDK, [email protected]
MS76
Slow Dynamics in Balanced Networks withDistance-dependent Connections
We investigate the relationship between the spatial de-pendence of connections in networks of excitatory and in-hibitory neurons and the dynamics of the network. We findthat long timescale behavior in which spatially localizedclusters of neurons transiently increase their firing ratesare promoted by a spatially dependent connection struc-ture, particularly when the spatial scale of inhibition isbroader than excitation. These dependencies unveil pop-ulation dynamics not present in neuronal networks with
180 DS11 Abstracts
homogeneous connection probabilities.
Ashok L. KumarCarnegie Mellon [email protected]
Brent DoironDept. of MathematicsUniv. of [email protected]
MS76
The Case Against Common Input: Why Conver-gence and Chains are Network Structures thatInfluence Synchrony in Recurrent Neuronal Net-works
We investigate the influence of network structure on thetendency for neuronal networks to synchronize. The anal-ysis is based on the framework of second order networks, anetwork model that captures second order statistics (cor-relations) among network edges. We demonstrate how thefraction of common input onto pairs of neurons, when un-correlated with other network properties, has little effect onnetwork synchrony, even in networks with only excitatoryneurons. In contrast, both the degree of network conver-gence and the relative frequency of network chains have aprofound influence on network synchrony. Insight into thecritical role of chains when combined with convergence andcommon input can be explained by a pool and redistributemechanism. Increased chain connections ensure that corre-lations in the network activity that are amplified throughthe input pooling of convergence are redistributed through-out the network, leading to the development of synchronyacross the network.
Duane NykampSchool of MathematicsUniversity of [email protected]
MS77
Stokes Regularization of the Laplacian Growth inHele-Shaw Cell
Recently it was shown that the cusp forming singularityof the Laplacian growth in a Hele-Shaw cell can be regu-larized by relaxing the incompressibility condition of theviscous liquid. Then at the end one can restore the in-compressibility and find a weak solution of the Laplaciangrowth beyond singularities. In this talk I will show thatthis procedure corresponds to the real physics of the flowin a Hele-Shaw cell.
Artem G. AbanovPhysics Department,Texas A&M [email protected]
MS77
Interface Motion of Evaporating Thin Films
A thin water film on a cleaved mica substrate undergoes afirst order phase transition between two values of film thick-ness. By inducing a finite evaporation rate of the water,the interface between the two phases develops a fingeringinstability similar to that observed in the Saffman-Taylorproblem. A key role in the evolution of the interface is
played by an additional instability that appears along theinterface. It is similar to Rayleigh instability, but unlikethe extended undulations of the Rayleigh instability, it islocalized to the regions of maximum curvature.
Oded AgamThe Racah Institute of PhysicsThe Hebrew [email protected]
MS77
The Exponential Transform in 2D
The power moments of a planar shape, or even a shadefunction, can be optimally arranged into a formal seriestransform which involves non-linear algebraic operations.The relevance of this (exponential) transform for recon-struction, approximation and qualitative estimates will bepresented in parallel with a few basic examples.
Mihai PutinarUniversity of California, Santa BarbaraMathematics [email protected]
MS77
Interface Motion in a Hele-Shaw Cell and a Dy-namical Mother Body
We start with a quick review of the state of the art of the in-terface motion problems and show the connections betweenHele-Shaw problem and other applications of the Laplaciangrowth in physics. We discuss negative Laplacian growth,introducing a dynamical mother body and presenting analgorithm and examples of a complete removal of a fluiddroplet with algebraic boundary from a Hele-Shaw cell.
Tatiana SavinNorthwestern [email protected]
Alexander NepomnyashchyDepartment of [email protected]
MS78
Critical Slowing Down As An Indicator of DynamicInstability in Power Systems
With the growing deployment of synchronized phase-anglemeasurement units (PMUs) in power systems, there is arapidly increasing quantity of high resolution, time syn-chronized sensor data available to system operators. Infor-mation in these data that could signal a critical transition,such as voltage collapse or dynamic instability, could bevaluable to system operators who need to make timely, andcostly, decisions to avert large blackouts. This talk will pro-vide preliminary evidence that time-series data alone, with-out intricate network models, can signal a pending criticaltransition in power systems. We will discuss theoreticalresults for a two-bus model illustrating how recovery timesincrease as proximity to criticality decreases, and empiricalresults for the August 10, 1996 blackout in Western NorthAmerica.
Paul Hines, Eduardo Cotilla-SanchezUniversity of [email protected], [email protected]
DS11 Abstracts 181
MS78
Inverse Problems in Power System Dynamics
Analysis of power system dynamic behavior frequentlytakes the form of inverse problems, where the aim is tofind parameter values that achieve (as closely as possible)a desired response. Examples range from parameter esti-mation to various forms of boundary value problems. Thetalk will consider algorithms for solving inverse problems,and in particular will focus on locating limit cycles andgrazing phenomena. Power system behavior inherently in-volves interactions between continuous dynamics and dis-crete events. A systematic hybrid systems framework formodeling, analysis and algorithms will be presented.
Ian HiskensUniversity of [email protected]
MS78
Cascading Dynamics of Power Grid Networks
Large blackouts in power networks are typically caused bycascading processes triggered by small number of initialfailures in the network. Based on the simulations of mi-croscopic model of power flows we analyze the dynamicsof the cascades. We show that the dynamics is essentiallynon-local and can not be modeled by the disease-spreadtype models. The algebraic distribution of blackout sizeis directly related to the hierarchical structure of powergrids. We analyze the effect of future ”smart” technologieson the cascade dynamics, and propose specific approachesfor mitigating the damage caused by the cascade.
Konstantin [email protected]
MS79
Overview of Sleep-Wake Regulation and Dynamics
A number of brainstem and hypothalamic neuronal popu-lations, as well as the neurotransmitters they express, con-tribute to the regulation of sleep-wake states. However,different structures for the sleep-wake regulatory networkhave been proposed with particular debate over compo-nents involved in REM sleep regulation. This overviewwill discuss the competing regulatory network structures,a firing rate model formalism for network modeling andhow analysis of the temporal dynamics of sleep-wake pat-terning may inform network structure.
Victoria BoothUniversity of MichiganDepts of Mathematics and [email protected]
MS79
Mechanisms for Controlling REM Sleep Patterns
We present a minimal mathematical model of sleep wake-fulness. The model demonstrates the plausibility of dif-ferent mechanisms that control the transition to and fromREM sleep. Each mechanism is shown to have specificconsequences regarding the frequency and length of REMbouts within a sleep-wake cycle and within the larger cir-cadian rhythm. The potential roles of pre-synaptic inhibi-tion and synaptic plasticity will be discussed. The primarymathematical tools are those of geometric singular pertur-
bation theory.
Amitabha BoseNew Jersey Inst of TechnologyDepartment of Mathematical [email protected]
MS79
Ultradian Dynamics in a Potential Formulation ofHuman Sleep
Mammalian sleep is characterized by ultradian oscilla-tions between rapid eye movement (REM) and non-REM(NREM) stages, but the underlying physiological mech-anism is unknown. Previously we showed that humansleep/wake dynamics can be reproduced by a particle ina one dimensional nonconservative quartic potential, withstable states corresponding to wake and sleep. We extendthis to two dimensions, representing wake/sleep state byposition in the first dimension, and REM/NREM state byposition in the second dimension.
Andrew PhillipsBrigham & Womens Hospital, Harvard Medical [email protected]
Peter RobinsonSchool of PhysicsUniversity of [email protected]
Elizabeth KlermanBrigham & Womens Hospital, Harvard Medical Schoolelizabeth [email protected]
MS79
Modeling the Human Sleep-Wake Cycle
We present a biologically-based mathematical model thataccounts for several features of human sleep and demon-strate how particular features depend on interactions be-tween a circadian pacemaker and a sleep homeostat. Themodel is made up of regions of cells that interact witheach other to cause transitions between sleep and wake aswell as between REM and NREM sleep. Analysis of themathematical mechanisms in the model yields insights intopotential biological mechanisms underlying sleep.
Michael RempeMathematics and Computer Science DeptWhitworth University, Spokane [email protected]
Janet Best, David H. TermanThe Ohio State UniversityDepartment of [email protected], [email protected]
MS80
Measuring the Response of Species Interactions toClimate Change: The Use of Models and Experi-ments to Study Seed Dispersal by Ants
We developed a temperature-dependent model of seed dis-persal by ants. We use the model to evaluate how we canuse a multi-year experiments in Duke and Harvard Forestto predict the persistence of the seed dispersal by ants un-der future warming scenarios. We will present the current
182 DS11 Abstracts
results of the experiment and related model analysis andwe will examine the long-term effects that climate changewill have on seed dispersal by ants in temperate forests.
Judith CannerDepartment of Mathematics and StatisticsCalifornia State University at Monterey [email protected]
MS80
Competitive Outcomes Changed by Evolution
Using evolutionary game theory, we investigate how evolu-tion can change the outcome of a competitive interactionbetween two species. We focus on changes from competi-tive exclusion to coexistence and from the exclusion of onespecies to the other. There are two crucial factors: therate of evolution and what we term the boxer effect. Weapply the theory to data from two historical competitionexperiments and show how it can explain certain seeminglyanomalous results.
Jim M. CushingDepartment of MathematicsUniversity of [email protected]
Rosalyn RaelDepartment of Ecology and Evolutionary BiologyUniversity of [email protected]
Thomas VincentUniversity of [email protected]
MS80
Niche Construction and Sustainability in Resource-dependent Competition Models
In a heterogeneous population, where each individual hasaccess to the common resource, sustainability may becomean issue if some choose to take more than they give back.We study this situation through a dynamical system model,where we identify a sustainability threshold and a series oftransitional pre-extinction dynamic regimes as parametersare varied is identified. We observe that 1) heterogeneouspopulation survives longer than a homogeneous populationand 2) high natural decay rate of the resource allows ex-istence of more aggressive super-consumers without goingextinct, most probably due to the fact that in such an envi-ronment even very aggressive super-consumers can’t reachthe resource quite soon enough as to exhaust it.
Irina KarevaInstitute for Applied Mathematics for Life and SocialSciencArizona State [email protected]
MS80
Management and Dynamics in a Predator-PreyMetapopulation
Increased landscape fragmentation has a deleterious ef-fect on terrestrial biodiversity. There is a push to tran-sition from developing protected areas to policies sup-porting corridor management. Given the complexities of
multi-species interactions, managers need additional toolsto aid in decision-making and policy development. We de-velop theoretical and agent-based models of a two-patchmetapopulation with local predatory-prey dynamics andvariable density-dependent species migration. The goal isto assess how connectivity of a patch promotes species con-servation.
Kehinde SalauArizona State [email protected]
MS81
Contact Bifurcations of Invariant Absorbing Setsand Basins in Noninvertible Maps
Contact bifurcations of chaotic attractors and their basinsare considered, both in 1D an 2D noninvertible maps.When invariant sets are bounded by critical sets, then theircontacts with the boundary of the immediate basin leadsto some homoclinic bifurcation (of saddles or repelling ex-panding points) causing a change in the dynamic behavior.Moreover, contacts of critical sets with basins’ boundariescan cause global bifurcations that change the topologicalstructure of basins, leading to multiply connected or nonconnected basins. Some applications to discrete time dy-namic modelling of economic and social systems are shown.
Gian Italo Bischi, Laura GardiniUniversity of UrbinoDepartment of Economics and Quantitative [email protected], [email protected]
MS81
Interacting Global Manifolds in a Planar MapModel of Wild Chaos
We consider a planar noninvertible map that has been sug-gested as a model for wild chaos. This map opens up theorigin to a bounded domain and wraps the plane twicearound it. We study stable and unstable manifolds in thetransition to (wild) chaos. A new aspect is their inter-action with the critical set consisting of the images andpreimages of the origin which are closed curves and pointsrespectively.
Stefanie Hittmeyer, Bernd KrauskopfUniversity of BristolDepartment of Engineering [email protected],[email protected]
Hinke M. OsingaUniversity of BristolDepartment of Engineering [email protected]
MS81
Connecting Period-doubling Cascades to Chaos viaManifolds in Phase Cross Parameter Space
The appearance of infinitely-many period-doubling cas-cades is one of the most prominent features observed indynamical systems varying with a parameter. Bifurcationdiagrams often reveal the intermingling of cascades andchaos. Our recent research rigorously links cascades andchaos using a one manifold of periodic orbits in phase cross
DS11 Abstracts 183
parameter space. Our examples include iterated maps aris-ing from Poincare sections of both finite-dimensional flowsand infinite-dimensional delay-differential equations.
Evelyn SanderGeorge Mason [email protected]
James A. YorkeUniversity of MarylandDepartments of Math and Physics and [email protected]
Madhura JoglekarUniversity of [email protected]
MS81
Global Dynamics Using Parameter-sweeping Tech-niques
In this talk we present, via several paradigmatic examples,such as the Lorenz and Rossler models, how we can obtainparametric studies of the systems by the combined use ofdifferent numerical techniques. These numerical results arebased on parameter-sweeping techniques on the completethree-parameter space of the systems, and they permit toexplain some of the global dynamics of the models.
Sergio Serrano, Roberto BarrioUniversity of Zaragoza, [email protected], [email protected]
Fernando BlesaUniversity of [email protected]
MS82
Homoclinic Snaking: Overview, Recent Progressand Open Questions
In this talk I shall review applications of so-called homo-clinic snaking in buckling, pattern formation and opticalcavities. The fundamental ingredients are a heteroclinicconnection between an equilibrium and a periodic orbit ina reversible systems. Two recent developments are consid-ered including the combined effect of discreteness and dis-sipation and the possibility of a new kind of snaking withvery different asymptotics, where the edges of the snake oc-cur at a fold in the central periodic state. The latter caseis analysed in detail. Throughout the talk open questionsare highlighted.
Alan R. ChampneysUniversity of [email protected]
MS82
1D Localized Structures in Bounded Domains inthe Lugiato-Lefever Model
We analyze the influence of boundaries on localized struc-tures in a large but finite optical cavity. Analytical re-sults are derived in a general context in the framework ofthe Swift-Hohenberg equation, where the stable localizedpatterns arise from a Turing bifurcation [G. Kozyreff, P.Assemat and S.J. Chapman, Influence of Boundaries onLocalized Patterns, Phys. Rev. Lett. 103, 164501 (2009)].
For almost any boundary condition, we find that they canonly be stably located in a discrete set of locations. Multi-peak solutions are rapidly constrained to sit in the middleof the domain as their size increases. Moreover, single-peak solutions only exist sufficiently far from the edges ofthe domain. These features are predicted and confirmednumerically in the Lugiato-Lefever model.
Lendert GelensTONA, Vrije Universiteit BrusselB-1050 Brussels, [email protected]
Gregory KozyreffOptique Nonlineaire , Universite Libre de BruxellesCP 231, Campus Plaine, B-1050 Bruxelles, [email protected]
MS82
Multi-pulse Solutions in the Swift-HohenbergEquation
Single pulse solutions of the Swift-Hohenberg equation(SHE) have been extensively studied and their origin andbifurcation structure is now well understood. The case ofmulti-pulse solutions is much more complex. We discussthe existence and bifurcation structure for multi-pulse so-lutions. By imposing a left-right symmetry breaking onthe SHE we show how multi-pulse states are all connectedin parameter space.
Steve HoughtonUniversity of Leeds, United [email protected]
Thomas WagenknechtUniversity of [email protected]
MS82
Defect-mediated Snaking: Spatial and TemporalDynamics
In the 1:1 forced complex Ginzburg-Landau equation,steady localized states undergo defect-mediated snaking(DMS) where new rolls of periodic states are nucleatedat the center of the wave train. The onset of DMS resultsfrom interaction between a heteroclinic orbit connectingtwo equilibria and a supercritical Turing bifurcation onone of them. As another parameter is varied, DMS breaksinto isolas away from onset, while the temporal dynamicschange from depinning to pulse interaction.
Yiping MaDepartment of PhysicsU. C. [email protected]
Edgar KnoblochUniversity of California, [email protected]
MS83
Alignment Dynamics and Its Effects on EffectiveViscosity of Bacterial Suspensions
We present results on suspensions of swimming bacte-ria with the focus on explaining their remarkable effec-
184 DS11 Abstracts
tive rheology: the effective viscosity of a bacterial sus-pension can be lower than that of a suspension of com-parable passive particles by nearly an order of magnitude[Sokolov and Aronson, Phys. Rev. Lett. 2009]. This be-havior stems from the emergence of collective swimming,which leads to coherent injection of energy and momen-tum into the fluid. Collective modes arise mostly due to ahydrodynamically-induced alignment between neighboringparticles.The mechanism and nature of alignment is inves-tigated analytically and computationally in the dilute andsemi-dilute limits, where the particles do not interact, orinteract via a mean field, respectively. An important rolein the explanation of the anomalous viscosity is played bythe presence of noise due to stochastic effects (bacterialtumbling, Browninan effects) or the effective noise due tointeractions. We further emphasize the importance of ex-cluded volume effects that help explain the rise in the ef-fective viscosity at higher particle concentrations, whichare not captured by point particle models. Additionally, inthe semi-dilute (mean field) regime we also investigate theeffects of anomalous diffusion, which has been observed ex-perimentally [Wu and Libchaber, Phys. Rev. Lett., 2000].Effective diffusivity acts as an additional source of effectivenoise, which helps explain the difference in the rheology ofpullers and pushers.
Dmitry KarpeevArgonne National [email protected]
Leonid BerlyandPenn State UniversityEberly College of [email protected]
Igor AronsonMaterials Science DivisionArgonne National [email protected]
Brian Haines, Shawn RyanDepartment of MathematicsPenn State [email protected], [email protected]
MS83
Simulations Versus Experiments on the Rheologyof Active Suspensions
The measurement of a quantitative and macroscopic pa-rameter to estimate the global motility of a large popula-tion of swimming biological cells is a challenge. The rhe-ology of suspensions containing such cells is a good can-didate. As a matter of fact, we recently performed rhe-ological measurements on suspensions of micro-algae [Ef-fective viscosity of microswimmer suspensions.S. Rafai, L.Jibuti, P. Peyla Phys. Rev. Lett., 104, 098102(2010)].Chlamydomonas Reinhardtii. These experiments showedthe strong effect of the microscopic swimming [Randomwalk of a swimmer in a low-Reynolds-number mediumMichael Garcia, Stefano Berti, Philippe Peyla and SalimaRafai To be published in Phys. Rev. E Rapid Comm.(2011)] on the macroscopic effective viscosity. The chosenalgae are pullers since they use two front flagellae to pull onthe fluid in a breast stroke motion. We discuss the severalmodels that have already predicted such behaviors and weshow different numerical simulations concerning the algasuspensions. We use these simulations in order to discrim-inate the relevant ingredients of the modelisation of the
algae puller-like suspensions.
Philippe PeylaUniversite Joseph [email protected]
Levan JibutiUniversite Jospeh [email protected]
Salima RafaiUniversite Joseph [email protected]
MS83
Oxygen Transport and Mixing Dynamics in ThinFilms of Oxytactic Microorganisms
We investigate the dynamics in suspensions of oxytacticswimming microorganisms using two different kinetic mod-els: a gradient-detecting model, in which the swimmersdetect local oxygen gradients instantaneously, and a run-and-tumble model, in which the swimmers change theirrun-and-tumble frequency based on the temporal changesin the oxygen field they sample. Using three-dimensionalnumerical simulations, we study the behavior of such sus-pensions in thin liquid films surrounded by oxygen bathson both sides. As the microorganisms consume the dis-solved oxygen, gradients form causing them to swim to-wards the free surfaces where the oxygen concentration ishigher. We demonstrate the existence of a transition fromquasi-two-dimensional dynamics and pattern formation inthin films to chaotic three-dimensional dynamics as filmthickness increases. This transition, which was also previ-ously observed in experiments, is shown to be associatedwith an enhancement of oxygen mixing and transport intothe liquid.
David SaintillanUniversity of Illinois at Urbana-ChampaignDepartment of Mechanical Science and [email protected]
Amir Alizadeh PahlavanDepartment of Mechanical Science and EngineeringUniversity of Illinois at [email protected]
Barath EzhilanUniversity of Illinois at Urbana-ChampaignDepartment of Mechanical Science and [email protected]
MS83
An Overview of the Simulation-based Dynamics ofMicroswimmer Suspensions
We will discuss how hydrodynamic interactions betweenthe organisms can lead to large-scale correlations and col-lective behavior. Simulations and theory have illustratedhow the behavior scales with concentration, the importanceof the method of swimming used, the influence of run-and-tumble like motions of the organisms. The orientationalcorrelations of the microorganisms lead to many key phe-nomena. For organisms that do not tumble these inter-actions occur even for very low concentrations, consistentwith microrheology experiments.
Patrick Underhill
DS11 Abstracts 185
Rensselaer Polytechnic InstituteDepartment of Chemical and Biological [email protected]
MS84
A Dynamical Systems Analysis of Territorial Be-havior
We consider a territorial model based on Voronoi tessella-tions. For rectangular domains and for small populationsizes, we show that there can be distinct coexisting stableequilibrium configurations. Furthermore, by treating theaspect ratio of the rectangle as a bifurcation parameter,we numerically explore how stable and unstable equilib-rium configurations are related to each other. Results forthree agents are verified through experiments using robotswhich move according to a related territorial algorithm.
Jeff MoehlisDept. of Mechanical EngineeringUniversity of California – Santa [email protected]
Ronald VotelDept Aeronautics & AstronauticsStanford [email protected]
David A. BartonUniversity of Bristol, [email protected]
Takahide Gotou, Takeshi Hatanaka, Masayuki FujitaTokyo Institute of [email protected], [email protected], [email protected]
MS84
Role of the Interaction Graph Topology in the Evo-lution of Collective Migration
We use the perspective of evolution by natural selectionto investigate the collective migration problem, where in-dividuals in a group can respond to social information andto a costly environmental cue. We study the role of thesocial interaction topology on evolutionary outcomes anddemonstrate a minimum connectivity threshold for randominterconnection graphs to yield speciated outcomes in re-sponsive behavior. We study the adaptation of nodes onfixed graphs and how topology affects emergent results.
Darren Pais, Naomi E. LeonardPrinceton [email protected], [email protected]
MS84
Synchronization of Cows
The study of collective behavior—of animals, mechani-cal systems, or even abstract oscillators—has fascinated alarge number of researchers from observational geologiststo pure mathematicians. I consider the collective behav-ior of herds of cattle. I first discuss some results froman agent-based model and then formulate a mathematicalmodel for the daily activities of a cow (eating, lying down,and standing) in terms of a piecewise affine dynamical sys-tem. I analyze the properties of this bovine dynamical sys-tem representing the single animal and develop an exact
integrative form as a discrete-time mapping. I then couplemultiple cow ”oscillators” together to study synchrony andcooperation in cattle herds, finding that it is possible forcows to synchronize less when the coupling is increased.
Mason A. PorterUniversity of OxfordOxford Centre for Industrial and Applied [email protected]
MS84
Compensatory Perturbations for Network Dynam-ics
Networked systems often exhibit multiple coexisting stablestates. Some of these states may be preferred over others,but may not correspond to the state spontaneously real-ized by the system. A fundamental question is then toestablish methods to drive the system from one such stateto another under realistic constraints. We formulate thisopen problem in the context of dynamical systems and de-velop a general method that can be scaled to very largenetworks.
Jie Sun, Sagar Sahasrabudhe, Adilson E. MotterNorthwestern [email protected],[email protected],[email protected]
MS85
Dynamics at Infinity
We interpret phenomena like blow up or grow up as hetero-clinic connections between finite invariant sets and infinity— or “transfinite” heteroclinics. We access infinity by ap-plying the Poincare compactification projecting the phasespace on the Poincare hemisphere. Infinity is thereby pro-jected on its equator, an invariant sphere where infinity un-folds its “celestial” dynamics. The Conley index is a usefultool to analyze the connections structure and was success-fully applied on bounded global attractors. In the contextof unbounded dynamics, Conley index has to be adaptedcarefully to be able to detect transfinite heteroclinics: evensimple systems like planar quadratic ODEs show behav-iors near the sphere at infinity that prevent the isolationrequired by Conley index theory. In order of overcomingthis difficulty, we define the concept of “dynamical comple-ment” of an invariant set. The isolated invariance of thedynamical complement is our requirement for establishingthe existence of transfinite heteroclinics via non-classicalConley index techniques.
Juliette HellFreie Universitat BerlinInstitut fur [email protected]
MS85
Rigorous Numerics for Connecting Orbits for Flows
I will discuss a new method for computer assisted proofof the existence of connecting orbits for ordinary differen-tial equations. The method consists of reformulating theboundary value problem as a functional equation solved byorbits which begin on the unstable manifold of one equilib-ria and end on the stable manifold of another. We solve thefunctional equation using the method of Validated Contin-uation. A novelty of the scheme is the use of the Parame-
186 DS11 Abstracts
terization Method, which facilitates high order polynomialapproximation of the invariant manifolds and allows therigorous bounding of the truncation errors.
Jason Mireles JamesRutgers [email protected]
MS85
The Euler-Floer Characteristic and Forcing of Pe-riodic Points in Two-dimensional Diffeomorphisms
For area-preserving diffeomorphisms a finite set of peri-odic points allows the definition of braid Floer homologyrelated to mapping classes. If the braid Floer homology isnon-trivial this forces additional periodic points of a giventype and provides a Morse type theory. We show that cer-tain information contained in the Floer homology — theEuler-Floer characteristic — also forces periodic points ofarbitrary diffeomorphisms. These ideas are applied to thesimplest case of the 2-disc, but can easily be extend totwo-dimensional surfaces, with or without boundary.
Simone MunaoVU University [email protected]
MS85
Flow Categories
Morse theory studies the topology of manifolds throughMorse functions defined on them. One shows that a Morsefunction generates a CW-complex which is homotopic tothe manifold. Cohen, Jones, and Segal have shown thatit is possible to study this differently. From the flow theyconstruct a flow category, whose classifying space is homo-topic to the manifold. Filtrations of this category inducefiltrations of the manifold. We will discuss how to con-struct flow categories for general dynamical systems, andshow that the classifying space is homotopic to the under-lying space. We do not need any smoothness of the flow orof the underlying space. It is possible to derive relationsof Morse type, which force existence of invariant sets withcertain topologies.
Thomas RotVU University AmsterdamDepartment of [email protected]
MS86
Discovery of Cellular Mechanisms and Prognosisof Cancers from Mathematical Modeling of DNAMicroarray Data
In my lab, we develop novel matrix and tensor computa-tions for comparison and integration of multiple genomicdatasets recording different aspects of, e.g., the cell di-vision cycle and cancer. Our recent experiments verifiedthat modeling DNA microarray data by using these com-putations can correctly predict previously unknown mech-anisms. Our recent computational prognosis of tumorsfrom the Cancer Genome Atlas draws a mathematical anal-ogy between the prognosis of disease and the prediction ofglobal cellular mechanisms.
Orly AlterUSTAR Assoc Prof of Bioeng & Sci Comp & Imaging(SCI)
University of [email protected]
MS86
Master Stability Function Approach for DesigningSynchronous Networks
The master stability function (MSF) is a mathematical toolfor determining if a given configuration of coupled chaoticoscillators will synchronize. By decoupling the network dy-namics from the individual equations for each of the chaotictrajectories, the MSF reveals the stability of a globally syn-chronous solution using only the eigenvalues of the adja-cency matrix. In this talk, we analyze the stability of anadaptive method that can maintain synchrony even whencoupling strengths are time-varying.
Adam B. Cohen, Bhargava RavooriUniversity of Maryland, College ParkDept. of [email protected], [email protected]
Francesco SorrentinoUniversita degli Studi di Napoli [email protected]
Thomas E. MurphyUniversity of Maryland, College ParkDept. of Electrical and Computer [email protected]
Edward OttUniversity of MarylandInst. for Plasma [email protected]
Rajarshi RoyUniversity of [email protected]
MS86
Principal Component Analysis of the Water WaveProblem
We consider the dynamics and stability of time-periodicstanding surface gravity waves using a dimensionality re-duction technique based on the Proper Orthogonal Decom-position (POD). The reduced model qualitatively repro-duces the entire solution branch, from the low-amplitudesinusoidal solutions to the high-amplitude solutions withsharply peaked crests, thus demonstrating that the time-periodic standing wave solutions, along with their bifurca-tions structure and stability, can be considered in a low-dimensional framework when the proper basis is selected.
J. Nathan KutzUniversity of WashingtonDept of Applied [email protected]
MS86
Proper Orthogonal Modes for the Muti-Pulsing In-stability in a Mode-Locked Laser Cavity
The multi-pulse transition is studied with a low dimen-sional model constructed by the method of proper orthog-onal decomposition. The specific model employed uses awaveguide array as the cavity saturable absorber. The
DS11 Abstracts 187
bifurcation structure of the multi-pulse transition is de-termined, starting with the single-pulse solutions up untilthe Neimark-Sacker bifurcation that initiates the route tochaos. Lastly, the predictions of low dimensional model arecompared with the transition in the full PDE.
Matthew O. WilliamsApplied MathematicsUniversity of [email protected]
Eli ShlizermanUniversity of [email protected]
J. Nathan KutzUniversity of WashingtonDept of Applied [email protected]
MS87
Piecewise-smooth Neural Fields with NonlinearAdaptation
We analyze traveling wave and stationary bump solutionsof a piecewise-smooth neural field model with synaptic de-pression. The continuum dynamics is described in termsof a nonlocal integrodifferential equation, in which the in-tegral kernel represents the spatial distribution of synapticweights between populations of neurons whose mean firingrate is taken to be a Heaviside function of local activity.Synaptic depression dynamically reduces the strength ofsynaptic weights in response to increases in activity. Weshow that the local stability of a stationary bump is de-termined by solutions to a system of pseudo-linear equa-tions that take into account the sign of perturbations ofthe bump boundary. Traveling wave solutions introduceadditional smoothing. Applications to the spatiotemporaldynamics of binocular rivalry are presented.
Paul C. BressloffUniversity of Utah and University of Oxford, UKDepartment of [email protected]
Zachary KilpatrickUniversity of [email protected]
MS87
Finite Size Effects in Spiking Neural Networks
Neural networks with biophysical spiking neurons are gen-erally described by large systems of ODEs that are diffi-cult to analyze. The classical way to make the problemmore tractable is to reduce it to a population rate descrip-tion such as the Wilson-Cowan equations. However, thesereductions take an infinite size mean field limit and thusignore the effects of fluctuations and correlations. Here, Iwill describe a new formalism that allows for a systematicexpansion of a coupled network of quadratic integrate-and-fire neurons that accounts for system size effects.
Carson C. ChowLaboratory of Biological ModelingNIDDK, [email protected]
Michael Buice
LBM/NIDDKNational Institutes of [email protected]
MS87
A Network of Sparsely Active Interneurons Initi-ates Retinal Waves
The developing nervous system generates spontaneous ac-tivity that has a periodicity on the order of minutes. Whatare the cellular mechanisms that give rise to these infre-quent network events? Using electrophysiological and cal-cium imaging approaches, we have characterized the cellu-lar properties of neurons that give rise to spontaneous reti-nal waves in the developing retina. These pacemaker neu-rons, called starburst amacrine cells, spontaneously depo-larize in the absence of synaptic connections at a rate thatis an order of magnitude less frequent than the networkactivity. Strong connections between neighboring cells re-sult in the ability of single cells to initiate a wave. Spatialpropagation extent and initiation rates are restricted bya slow afterhyperpolarization in starburst cells. Using aconductance based model of a network of starburst cells,we demonstrate that the robust spatial and temporal fea-tures of waves can be reproduced by a network of sparselyactive cells only when variability in synaptic connectiv-ity between neighboring cells is modeled. In addition, themodel accurately predicts how wave features are altered byexperimental manipulations of spontaneous depolarizationrate and the slow afterhyperpolarization. By comparingmodels with different cellular behavior that correspond tomeasurements from different species, we find that disparatecellular properties can interact to give rise to network levelactivity with highly similar features.
Kevin Ford, Marla FellerUniversity of California [email protected], [email protected]
MS87
Neural Activity Measures and Their Dynamics
We provide an asymptotically justified derivation of evolu-tion equations for activity measures of a neural network.The derivation is based upon neurons’ first principal dy-namics, i.e. the Hodgkin-Huxley equations or their reduc-tions. The resulting equations serve as a dimension re-duction for the complicated network when the dynamicsare attracted to a synchronized solution. Computationalresults of the mean measure evolution equation for a net-work of identical FitzHugh-Nagumo neurons validate theapproach and its underlying assumptions.
Eli Shlizerman, Konrad SchroderUniversity of Washington, [email protected], [email protected]
J. Nathan KutzUniversity of WashingtonDept of Applied [email protected]
MS88
Macroscopic Physiology
Human physiology, as a science, aims to understand themechanical, physical, and biochemical functions of humans;moreover, because human dynamics transpire both on mul-
188 DS11 Abstracts
tiple spatial scales, ranging from molecular, to cell, to or-gan, to collections of organs and on multiple time scalesranging from fractions of a second to decades, it is likelythat complete models of human functioning will consist ofhighly complex models whose scales interact in complexways (via e.g., nonlinear resonance). While, mathematicalmodeling of physiological systems on the cellular and or-gan scales has a long history, integrating long time-scaledata analysis with the physiological modeling is largelynon-existent. It is of course no mystery why this is thecase; such long-time data has been difficult or impossi-ble to collect; fortunately, with the advent and increasinguse of electronic health records (EHR), the data existenceroadblock will be largely removed and replaced with scien-tific and methodological problems. Broadly, this talk takesaim at outlining some first steps in constructing an inter-face between EHR temporal data, which typically containstime-scales of hours to years, and the modeling of humanphysiological systems. More particularly, this talk will fo-cus on the glucose-insulin regulation system.
David AlbersColombia [email protected]
MS88
Amoeba-based Neurocomputing and Resource-Competing Oscillator Networks
A single-celled photosensitive amoeboid organism, the trueslime mold Physarum, exhibits rich spatiotemporal oscil-latory behavior and sophisticated computational capabil-ities. Applying optical feedback according to a recur-rent neural network model, the amoeba can be used asa computing substrate to explore solutions to the travel-ing salesman problem. We show the experimental resultsand introduce our mathematical models that reproduce theamoeba-like spatiotemporal oscillatory dynamics appliedto solve some optimization problems in resource allocationand decision-making.
Masashi AonoASI, [email protected]
MS88
EHR Dynamics: An Introduction
Data sets that represent population-wide, temporal, hu-man health dynamics are just beginning to come into ex-istence in the form of electronic health records (EHRs).Because these data include a range of time scales fromminutes to decades, and will, in the future, span the earth,the possibility of studying and modeling human function-ing on larger time and spatial scales much as climatologydoes for atmospheric physics will become a reality. Saiddifferently, humans are the ultimate model organism, andEHRs are the key to studying their medium- to long-termtime and spatial scales. These data come with a compli-cation, however. EHR data are not collected for scientificresearch, and more importantly, they are not collected in acontrolled environment. Therefore, an EHR not only con-tains measurements of a natural system, but it is a naturalsystem. In particular, EHRs depend on their location onthe planet, their internal rules (e.g., their internal measure-ment dynamics), their population, and many other internaland external factors. This talk introduces EHR data as adynamical structure as well as some of the problems incor-porated into the use of EHRs as a data source. Along the
way, a set of new, unique, nonlinear time-series analysisproblems will be identified.
George HripcsakDepartment of Bioinfomatics, Columbia [email protected]
MS88
Noise-induced Phenomena in One-dimensionalMaps
Problems of complex behavior of random dynamical sys-tems is investigated based on numerically observed noise-induced phenomena in Belousov-Zhabotinsky map (BZmap) and modified Lasota-Mackey map with presence ofnoise. We found that (i) both noise-induced chaos andnoise-induced order robustly coexist, and that (ii) asymp-totical periodicity of density is varied according to noiseamplitude. Applications to time series analysis are alsodiscussed.
Yuzuru SatoRIES, Hokkaido [email protected]
MS89
Rules Versus Optimization for Enabling AdaptiveNetwork Topologies
A fully-enabled smart transmission grid could allow adjust-ment of network topology in real-time, increasing opera-tional efficiency. Meta-analysis of previous mixed-integer-based approaches suggests that most efficiency gains arisefrom small changes in topology; are invariant to the levelof demand; and appear to be localized in nature. We pro-pose a rule-based framework for enabling flexible topolo-gies based on network partitioning. Our method couldbe implemented quickly, while optimization algorithms formixed-integer problems are further developed.
Seth Blumsack, Clayton BarrowsPennsylvania State [email protected], [email protected]
MS89
Modeling and Control of Aggregated Heteroge-neous Thermostatically Controlled Loads for An-cillary Services
This talk presents a novel modeling and control approachfor the aggregation of large numbers of heterogeneous ther-mostatically controlled loads, such as refrigerators, electricwater heaters, and air conditioners, and their usage forDemand Response. Unlike traditional Demand Responsemethods that act on time scales of hours, this approach isable to provide short-term (e.g., second-to-second) ancil-lary services, such as balancing and frequency control. Astatistical modeling approach based on Markov Chains isused to describe the evolution of probability mass in a tem-perature state space. The Markov state transition matrixis identified using both (1) full state information and (2)information from only a subset of loads. A predictive con-troller is used to control the aggregate population of loadssuch that it tracks a signal. A simulation example showsthe applicability of the approach to realistic systems, andincludes a comparison of control performance dependingon available state information.
Duncan Callaway
DS11 Abstracts 189
University of California, [email protected]
Stephan KochETH [email protected]
Johanna MathieuUC [email protected]
MS89
Demand Response to Uncertainty in RenewableEnergy
A utility company plays in multiple wholesale electricitymarkets, including day-ahead market and real-time balanc-ing market to provision aggregate power to meet demandsand then retails it to end users. It aggregates demandso that the wholesale markets can operate more efficientlyand it absorbs large uncertainty and complexity of genera-tion and translate them into a much simpler environmentboth in prices and supply for the retail users. We pro-pose a model that captures these features. We analyzea demand response scheme that can be implemented in adistributed manner and converges almost surely to a social-welfare maximizing solution.
Steven Low, Libin [email protected], [email protected]
MS89
Modeling and Simulation of a Renewable and Re-silient Electric Power Grid
Electricity and the electric grid will play a crucial role inour transition to a sustainable energy infrastructure. Inte-grating a significant percentage of renewable energy sourcesinto the nations energy mix, and delivering it through elec-tric transmission and distribution systems is a major re-search challenge since these sources are less controllablethan the fossil-fuel-based generation they will displace. Si-multaneous with these changes is the need to make theelectric grid even more resilient in order to insure maxi-mum continuity of electric service, even during severe sys-tem disturbances. This paper focuses on the modeling andsimulation aspects of these problems.
Thomas OverbyeUniversity of Illinois, [email protected]
MS90
Modeling Circadian Modulation of Sleep-wakeRegulatory Dynamics
Recent experimental advances have identified both feed-forward and feedback components involved in neuronal in-teractions between the suprachiasmatic nucleus and sleep-wake regulatory systems. Using a novel network modelingframework, we investigated interactions among neuronalnuclei involved in rat sleep-wake and circadian regulation.Fast/slow analysis of model dynamics reveals hysteresis viaa bursting-like bifurcation structure. This structure sug-gests mechanisms for dynamic influences of the circadianpacemaker on sleep-wake patterning, particularly the tim-
ing of rapid eye movement sleep.
Cecilia Diniz BehnUniversity of MichiganDept of [email protected]
Michelle FleshnerDept of MathematicsUniversity of [email protected]
Daniel ForgerUniversity of [email protected]
Victoria BoothUniversity of MichiganDepts of Mathematics and [email protected]
MS90
Data Assimilation in Sleep Models - a NonlinearEnsemble Kalman Approach To Tracking and Pre-dicting State
There have been extensive efforts to translate the biolog-ical understanding of the cellular elements of the sleep-wake regulatory system into mathematical/computationalmodels. We hypothesize that state of that system - andthe neurotransmitters it uses to modulate cortical state -could be useful for understanding seizure generation. Wewill report on our efforts to put these computational mod-els into a nonlinear ensemble-Kalman filter framework toassimilate data from long-term In-Vivo recordings.
Madineh Sedigh-Sarvestani, Steven Schiff,Bruce J. GluckmanPenn State [email protected], [email protected], [email protected]
MS90
High-resolution Sleep Scoring Through the Map-ping of EEG Onto a Cortical State Model
The current clinical method of sleep scoring involves divid-ing sleep into five discrete stages, which limits its diagnos-tic and predictive power. Using a dimensionality reductiontechnique (locally linear embedding) we show how humanEEG data can be mapped onto a representation of the sleepcycle within a nonlinear stochastic PDE mean-field corticalmodel. This evinces a continuous evolution through sleepstages and transitions over the course of a night.
Beth A. [email protected]
Savas TasogluUC [email protected]
Heidi E. KirschUC San [email protected]
James W. Sleigh
190 DS11 Abstracts
University of AucklandWaikato Clinical [email protected]
Andrew J. SzeriUC [email protected]
MS91
Analyzing Endogenous Thresholds in CoupledSocioeconomic-ecological Systems
Ecological thresholds are determined within a cou-pled socioeconomic-ecological system (SES) where humanchoices, including those of managers, are feedback re-sponses. Prior work assumes either that managers face noinstitutional constraints and thresholds are of little impor-tance, or that managers are rigidly constrained and thresh-olds can be describe as exogenous parameters. By model-ing institutions as a managers control set, we show thatthe location of thresholds in ecological state space dependson human institutions.
Rick HoranMichigan State [email protected]
Eli FenichelArizona State UniversitySchool of Life [email protected]
Kevin DruryBethel [email protected]
David LodgeNotre Dame [email protected]
MS91
A Model for the Spread of Animal Diseases withMitigation Strategies and a Case Study on Rinder-pest
Animal diseases are important in world economics, nationalsecurity, and biodiversity. We use a spatially explicit,hybrid (stochastic-deterministic) model for the spread ofmulti-host animal diseases in the United States with a casestudy on highly virulent rinderpest. We explore geographi-cal spread on a county level and different mitigation strate-gies. A forward sensitivity analysis indicates importantdisease parameters and containment approaches. General-izations of control strategies for rinderpest may be effectivefor other contagious animal diseases.
Carrie A. ManoreOregon State [email protected]
Benjamin McMahon, Jeanne FairLos Alamos National [email protected], [email protected]
James HymanTulane [email protected]
Mac BrownLos Alamos National [email protected]
Montiago LaButeLawrence Livermore National [email protected]
MS91
Optimal Management Controls for Maximizing theRecovery of an Endangered Fish Species
A computationally-expensiveindividual-based model (IBM) was used to simulate thepopulation decline of delta smelt during 1995 to 2005 in theUpper San Francisco Estuary. We approximated the IBMsoutput with a spatially-explicit matrix projection model.By applying optimal control theory to the matrix model,we determined cost-effective management actions involvingredirected movement and improved habitat (affecting mor-tality and growth) that would maximize long-term popu-lation growth during this period of decline.
Rachael Miller NeilanLouisiana State [email protected]
Kenneth RoseUniversity of [email protected]
Wim KimmererSan Francisco State [email protected]
William BennettBodega Marine LabUniversity of California, [email protected]
Karen EdwardsRomberg Tiburon Center for Environmental StudiesSan Francisco State [email protected]
MS92
Internal Modes and Instabilities of Solitons in theDiscrete NLS Equation
Discrete solitons of the discrete nonlinear Schrdinger(dNLS) equation are compactly supported in the anti-continuum limit of the zero coupling between lattice sites.Eigenvalues of the linearization of the dNLS equation atthe discrete soliton determine its spectral stability. Smalleigenvalues bifurcating from the zero eigenvalue near theanti-continuum limit were characterized earlier for thismodel. Here we analyze the resolvent operator and provethat it is bounded in the neighborhood of the continuousspectrum if the discrete soliton is simply connected in theanti-continuum limit. This result rules out existence of in-ternal modes (neutrally stable eigenvalues of the discretespectrum) near the anti-continuum limit.
Anton SakovichMcMaster [email protected]
Dmitry Pelinovsky
DS11 Abstracts 191
McMaster UniversityDepartment of [email protected]
MS92
Intrinsic Energy Localization Through DiscreteBreathers in One-dimensional Diatomic GranularCrystals
We present the possibility of energy localization in one-dimensional diatomic chains of tightly packed and uniaxi-ally compressed elastic beads. The localization is obtainedby the intrinsic nonlinearity, caused by the Hertzian inter-action of the beads, without additional inhomogeneities.We first characterize the linear spectrum of the system.We then use continuation techniques to find the exact non-linear localized solutions and study their linear stability indetail. Finally, we report the experimental observation ofthe energy localization in such media.
Georgios TheocharisCalifornia Institute of [email protected]
MS92
Breathers and Kinks in FPU Lattices
Combined breather-kink modes have been observed in sev-eral systems. We show that in the FPU lattice, small-amplitude breathing-kink modes are three-soliton solutionsof an associated mKdV equation. Since this is integrable,the modes can be constructed using the Backlund trans-form. As well as finding explicit solutions, we considerthe stability of the combined mode using variational tech-niques and illustrate stability for some parameter valuesand instability for others.
Jonathan WattisSchool of Mathematical SciencesUniversity of [email protected]
Andrew Pickering, Pilar R. GordoaDpt Matematica Aplicada, Universidad Rey Juan Carlos,[email protected], [email protected]
MS93
Continuation of Oscillons in an Autonomous Sys-tem of Reaction-diffusion Equations
We study the formation of oscillons in a model of theBelousov-Zhabotinsky reaction. We trace bifurcation di-agrams and compute stability of stationary localised spotsand find Hopf and fold bifurcations. We also continue os-cillons and show that, in some regions of the parameterspace, their period diverges as they approach a Shilnikovhomoclinic orbit. This suggests an alternative mechanismfor the formation of oscillons. This is joint work with D.Lloyd, K. Ninsuwan and B. Sandstede.
Daniele AvitabileDepartment of Mathematics, University of SurreyUniversity of [email protected]
MS93
Localised Patterns in a Crime Hotspot Model
It is shown that a PDE model of crime hotspots, derived byShort et al. from an agent-based stochastic model (Math.Model Meth. Appl. Sci. 2008), possesses localised patternsand homoclinic snaking. We analyse such patterns in thePDE model and also investigate what happens in the agent-based model. We then present recent efforts to investigatepatterns in the stochastic agent-based model by applyingthe equation-free methods of Kevrekidis et al. This work isjoint with Daniele Avitabile (Surrey), David Barton (Bris-tol), Rebecca Hoyle (Surrey) and Hayley O’Farrell (Surrey)
David LloydUniversity of [email protected]
MS93
Localized Patterns in the Swift-Hohenberg Equa-tion
The existence of localized structures in the two and threedimensional Swift–Hohenberg equation will be established.This is used as a model equation for pattern formation.These solutions are seen in mode-locked lasers, foliagegrowing patterns, and gas discharge systems. By usingnumerical continuation techniques where the dimension istreated as a continuous parameter, these solutions andtheir bifurcation structures were first seen. We will dis-cuss analytic proofs for the existence of these structures.
Scott McCallaDivision of Applied MathematicsBrown Universityscott [email protected]
MS93
Stability of Planar Layers in Reaction DiffusionEquations Coupled with a Conservation Law
We prove the stability of layers in systems exhibiting aconservation law coupled with a reaction diffusion equa-tion. The key element of the analysis is to find a homotopyto a lower-triangular PDE system that has stable solutionsand to control the essential spectrum during the homotopy.The layers can destabilize during the homotopy only in thecase when a Hopf bifurcation occurs. We use a Lyapunov-Schmidt analysis in weighted spaces to show that eigen-values can not pop out of or disappear into the essentialspectrum during the homotopy
Alin PoganUniversity of MinnesotaSchool of [email protected]
MS94
Collective Dynamics of Flagella and MultiflagellarOrganisms
Many bacteria have multiple helical flagella that self-assemble into bundles as they swim in fluid. We examinethe bundling process using a mathematical model of mul-tiple long slender flexible helical flagella in a fluid, withends either anchored or attached to a freely moving cellbody. A central result is that as parameters change, bifur-
192 DS11 Abstracts
cations between tight to loose bundles are found – multiplebundled states can coexist. Biological implications of ourresults are discussed.
Michael D. GrahamDept. of Chemical and Biological EngineeringUniversity of [email protected]
Pieter JanssenDept. of Chemical and BIological EngineeringUniversity of [email protected]
MS94
Boundary Effects on Continuum Models for ActiveSuspensions
We extend a recently developed continuum model of activesuspensions to a confined planar channel geometry. Wediscuss physical boundary conditions for the probabilitydistribution of allowable configurations for the center-of-mass and orientation, as well as modifications to the stressdistribution to include wall effects. We derive an evolutionequation for the system entropy, which shows that diffu-sion through the boundary modifies the stability resultsobtained for suspensions of pushers and pullers in a peri-odic box.
Christel HoheneggerUniversity of UtahDepartment of [email protected]
Michael J. ShelleyNew York UniversityCourant Inst of Math [email protected]
MS94
Random Flow in Suspensions of Swimming Algae
We have studied the random flow field induced by dilutesuspension of swimming algae Volvox carteri. The fluidvelocity in the suspension is a superposition of the flowfields set up by the individual organisms, which in turnhave multipole contributions that decay as inverse powersof distance from the organism. Here we show that the con-ditions under which the central limit theorem guarantees aGaussian probability distribution function of velocity fluc-tuations are satisfied when the leading force singularity isa Stokeslet for the far-field velocity. Deviations from Gaus-sianity for the tails of the distribution arise from near-fieldeffects. Comparison is made with the statistical proper-ties of abiotic sedimenting suspensions. The experimentalresults are supplemented by numerical simulation.
Vasily KantslerCambridge UniversityDepartment of Applied Mathematics and [email protected]
MS94
Constructive and Destructive Correlation Dynam-ics in Simple Stochastic Swimmer Models
A key observation derived from mean field theories for
micro-swimmers is the stability of the uniform isotropicstate for pullers vs. its instability for pushers. In sim-ulations of suspensions of swimmers, orientational corre-lations are apparent for pushers over much larger spatialscales than is observed for pullers. In this talk I will ex-amine the mechanisms that lead to large scale correlationsfor ”pusher-like” swimmers versus much smaller correla-tions for ”puller-like” in very simple stochastic swimmermodels.
Kajetan Sikorski, Peter R. KramerRensselaer Polytechnic InstituteDepartment of Mathematical [email protected], [email protected]
Patrick UnderhillRensselaer Polytechnic InstituteDepartment of Chemical and Biological [email protected]
MS95
Synchronization of Small Networks of Electrochem-ical Oscillators
Experiments are carried out with small networks of phasecoherent chaotic oscillators obtained with a chemical sys-tem of nickel electrodissolution in sulfuric acid. Three andfour oscillator setups are investigated in local and star cou-pling topologies. It is shown that (i) before transition tosynchronization the precision of the period strongly deteri-orates and (ii) bivariant and partial phase synchronizationindices are useful tools to delineate network structure fromdynamical measurements.
Istvan KissDepartment of ChemistrySaint Louis [email protected]
Mahesh WickramasingheSaint Louis [email protected]
MS95
Reactions of the Cell Cycle Network to MultipleStresses
All life forms have to survive long enough to reproduce andpass on their genes. This makes adaptations to the envi-ronment and the cell cycle pivotal for all life. I will dis-cuss a mathematical model which couples multiple stressresponse networks to the cell cycle. The model helps tounderstand why stress responses are not additive; it is pre-dictive of the stage of cell cycle arrest, and allows studyingthe robustness of the stress adaptation.
Elahe RadmaneshfarInstitute for Complex Systems and Mathematical BiologyUniversity of Aberdeen, [email protected]
Celso GrebogiKing’s CollegeUniversity of [email protected]
M. Carmen RomanoPhysics Department and Institute of Medical SciencesUniversity of Aberdeen
DS11 Abstracts 193
Marco ThielUniversity of [email protected]
MS95
Inferring Properties of Networks from Spike Trains
Spike trains have been shown to contain significant dy-namical information, and in some cases are sufficient toreconstruct attractors and estimate invariants. In this talkwe discuss recent progress in inference of network proper-ties from multivariate spike sequences, including networkconnectivity, state and basin determination, and data as-similation from spike times.
Tim SauerDepartment of MathematicsGeorge Mason [email protected]
MS95
Frequency Domain Based Estimations of Interac-tions Between Nonlinear Oscillators
Nonlinear systems are often characterized by oscillatory be-havior with a well-defined frequency. Various analysis tech-niques based on observations from these oscillators havebeen suggested. In several cases, however, the oscillatorsexhibit multiple time scales or are characterized by strongnoise influence. Here, we discuss a framework for the anal-ysis of such oscillators. Particular focus will be laid on theestimation of the strength of coupling between oscillators.Multivariate extensions will be presented.
Bjoern SchelterCenter for Data Analysis and ModelingUniversity of Freiburg, [email protected]
Marco ThielUniversity of [email protected]
M. Carmen RomanoPhysics Department and Institute of Medical SciencesUniversity of [email protected]
Linda SommerladeUniversity of [email protected]
Jens TimmerUniversity of FreiburgDepartment of [email protected]
MS96
Discontinuous Maps and Their Applications
Discontinous maps arise naturally in studies of non-smoothdynamical systems, either as descriptions of problems intheir own right (such as in models of active impacts) or
as natural simplifications of other maps, such as those en-countered in grazing bifurcations. In this talk we will showhow much of the global bifurcation thoery associated withgrazing problems can be described more easily using dis-continous maps. We will also show that the behaviourof systems with active impacts is extremely rich and thatthe robust chaos associated with grazing bifurcations ofcontinuous maps has a much finer structure when a smalldiscontinuity is introduced. Applications to impacting andswitching systems will be considered.
Chris BuddDept. of Mathematical SciencesUniversity of Bath, [email protected]
Karin MoraUniversity of Bath, [email protected]
MS96
Piecewise Smooth Systems, Set Valued Fields, andNondeterministic Chaos
Piecewise smooth systems model countless phenomena thatinvolve rapidly changing dynamic laws. Their solutionsare defined as solutions of a differential inclusion, and assuch can be non-unique. This well known detail is usuallyignored in applications, on the basis that forward-time non-uniqueness only affects sets that are not reachable fromgeneric initial conditions. A more careful look at systems inthree or more dimensions disproves this belief, revealing anentrance door into non-unique dynamics: these doors arecalled two-fold singularities. We will discuss new results onthe properties and applications of these singularities, whichare associated with interesting and novel bifurcations, andwith intricate dynamics that include what we are calling,in lack of a better word, nondeterministic chaos.
Alessandro ColomboMassachusetts Institute of [email protected]
MS96
Stasis Sets and Approximating Cycles
For a collection of C1 vector fields on Rn, points wherea linear combination of the fields sum to zero are calledstasis points. Generically, neighborhoods of such pointscontain cycles that switch between the vector fields, witha certain amount of freedom in choosing timing and orderof switches. We will discuss these results together with thestructure and bifurcations of the stasis set and approxi-mating families of cycles.
Stewart D. JohnsonDept of Mathematics and StatisticsWilliams [email protected]
MS96
TBA - Nordmark
Abstract not available at time of publication.
Arne NordmarkDepartment of MechanicsRoyal Institute of [email protected]
194 DS11 Abstracts
MS97
Parameterization of Invariant Manifolds for La-grangian Systems with Long-range Interactions
We generalize some notions that have played an impor-tant role in dynamics (namely invariant manifolds) to themore general context of difference equations. In particular,we study Lagrangian systems in discrete time. We defineinvariant manifolds, even if the corresponding differenceequations can not be transformed in a dynamical system.The results apply to several examples in the Physics lit-erature: the Frenkel-Kontorova model with long-range in-teractions and the Heisenberg model of spin chains with aperturbation. We use a modification of the parametriza-tion method to show the existence of Lagrangian stablemanifolds. This method also leads to efficient algorithmsthat we present with their implementations.
Hector E. LomeliInstituto Tecnologico Autonomo De Mexico (ITAM)[email protected]
Rafael de La LlaveUniversity of TexasDepartment of [email protected]
MS97
On the Lengths of Periodic Billiard TrajectoriesInside Axisymmetric Analytic Convex Tables
We present a numerical study of the asymptotic behaviorof the lengths of periodic billiard trajectories inside someaxisymmetric analytic strictly convex tables. We mainlyconsider tables of the form x2 + y2 + cyn = 1, for someinteger exponent n ≥ 3 and some real coefficient c. Weconjecture, based on the experiments, that inside any ax-isymmetric analytic strictly convex table there exist twoaxisymmetric q-periodic billiard trajectories whose lengthsare exponentially close in the period as q → +∞. Con-cretely, in all the computed cases the difference in lengthsis of order O(q−me−rq), for some exponents m ∈ {2, 3}and r > 0. Sometimes, it is possible to compute accuratedivergent asymptotic expansions for these differences. Wehave also considered tables of the form x2 + y4 = 1, whichare convex but not strictly convex. We show that thesetables show different asymptotic behaviors. The numericalexperiments get complicated due to problems of stability,precision and time, which require the use of a multiple pre-cision arithmetic.
Rafael Ramırez-RosDepartament de Matematica Aplicada 1Universitat Politecnica de [email protected]
MS97
Higher-order Adaptive Methods For ComputingInvariant Manifolds of Maps
We present efficient and accurate numerical methodsfor computing invariant manifolds of maps which arisein the study of dynamical systems. In order to de-crease the number of points needed to compute a givencurve/surface, we propose using higher-order interpola-tion/approximation techniques from geometric modeling.We use Bezier curves/triangles, one of the fundamental ob-jects in curve/surface design, to create an adaptive method.The methods are based on tolerance conditions derived
from properties of Bezier curves/triangles. We develop andtest the methods for ordinary parametric curves; then weadapt these methods to invariant manifolds of planar maps.Next, we develop and test the methods for parametric sur-faces and then we adapt this method to invariant manifoldsof 3D maps.
Jacek K. WrobelNew Jersey Institute of TechnologyDepartment of Mathematical [email protected]
Roy GoodmanNew Jersey Institute of [email protected]
MS98
When are pairwise maximum entropy methodsgood enough?
Recent experimental studies find that the activity patternsof many neural circuits are well described by pairwise max-imum entropy (PME) models — which require only the ac-tivity of single neurons and neuron pairs — even in caseswhere circuit architecture and input signals seem likelyto create a richer set of outputs. Why is this the case?We study spike patterns in feedforward circuits with dif-ferent architectures and inputs. Responses to unimodalinputs, regardless of connectivity, were well described byPME models; bimodal input signals drove significant de-partures. Circuits constrained by experimental data onretinal ganglion cells were well described by PME mod-els across a broad range of light stimuli, a fact explainedby experimentally quantified temporal filtering in synap-tic inputs. Preliminary results indicate that our resultsare highly dependent on the feedforward structure of thesecircuits; adding recurrent connections can enhance higherorder correlations 20-fold.
Andrea K. BarreiroDepartment of Applied MathematicsUniversity of [email protected]
Julijana GjorgjievaDepartment of Applied Mathematics and TheoreticalPhysicsUniversity of [email protected]
Fred RiekeUniversity of WashingtonPhysiology and [email protected]
Eric Shea-BrownDepartment of Applied MathematicsUniversity of [email protected]
MS98
A Kinetic Theory Model of Second Order Feedfor-ward Neuronal Networks
We aim to develop a kinetic theory model to capture the ef-fect of network structure on behavior characterized by thepopulation firing rates and pairwise correlations in sim-ple feedforward excitatory neuronal networks. We use a
DS11 Abstracts 195
recently proposed second order model to describe the feed-forward networks, where network structure is characterizedby covariance among connections. We demonstrate thatour developed kinetic theory model can capture the effectof network structure under the assumption of independencebetween in-degree and out-degree. The effect of in-out de-gree correlation, however, can not be captured by currentkinetic theory model. This presents a challenge for futuredevelopment of the kinetic theory model of second orderfeedforward neuronal networks.
Chin-Yueh LiuDepartment of Applied MathematicsNational University of Kaohsiung, [email protected]
Duane NykampSchool of MathematicsUniversity of [email protected]
MS98
Dynamical regimes of integrate-and-fire neuronalnetwork models
The dynamical regimes of a stochastically-driven, current-based Integrate-and-Fire neuronal network are investi-gated. A mean-field equation provide exact solutions forthe steady asynchronous state. The probability the net-work maintains a synchronous firing state is characterizedby the competition between the desynchronizing, noisy in-put, which drives each individual neuronal voltage andthe synchronizing instantaneous pulse-coupling betweenthe neurons in the network. For a prototypical scale-freenetwork, a detailed analytical calculation of clustering im-proves the usual tree-based second order theory.
Katherine NewhallRensselaer Polytechnic [email protected]
MS99
Stochastic Resonance and Noise-enhanced Phe-nomena in the Human Brain
Stochastic resonance, a nonlinear phenomenon in which theresponse of a system to a weak input signal is optimizedby noise, has been studied in many fields. We provide thefirst evidence that SR can enhance perceptual responsesto weak visual inputs in humans. We additionally demon-strate that the brain can be regarded as a coupled-oscillatorsystem and noise enhances synchronization of neural oscil-lators boosting information integration across widespreadbrain areas in the human brain.
Keiichi KitajoBrain Science Institute, [email protected]
MS99
Encoding of Slow Signals in High-pass Phasic Neu-rons with Background Fluctuations
Cortical processing occurs in the presence of many fluc-tuating excitatory and inhibitory inputs. We explore theeffects of these fluctuations on the encoding capabilitiesof phasic neurons that are known to respond well to highfrequency inputs and poorly to slow ones in vitro. Effi-
cient coding depends on robust responses to diverse stimu-lus profiles, yet the mechanism for encoding slow frequencysignals is unclear. We show that this can be achieved withbackground fluctuations in a modified Fitzhugh-Nagumomodel. A reduced model is developed to demonstrate thatnoise-induced encoding of slow signals can be achieved withhyperpolarizing inputs that effectively lowers the thresholdto response. The reduced model enables dissection of cru-cial mechanisms for fluctuation-induced encoding of slowtime-varying signals.
Cheng LyUniversity of PittsburghDepartment of [email protected]
MS99
Fluctuation of Brain Dynamics Related to Percep-tion
When repeatedly looking at an image, we may perceive itdifferently each time. This variation in perception is causedby the fluctuation of neural activity. By using non-invasiveneural activity recording technology, we have discoveredseveral links connecting neuronal activity and perception[Shimono et al., 2007, 2010]. In this presentation, I will in-troduce several experimental results related to importantconcepts in dynamical theory, such as noise, external con-trol, and information flow.
Masanori ShimonoPhysics Department, Indiana [email protected]
MS99
Long-tailed EPSP Distribution Reveals Origin andComputational Role of Cortical Noisy Activity
Cortical neurons exhibit irregular and asynchronous fir-ing spontaneously at low firing rates even without sensorystimuli.However, the mechanism to retain the stable noisyfiring remains elusive for networks of spiking neurons. Us-ing a simple integrate-and-fire model, we will show thatneural networks can stably generate low-rate asynchronousfiring when the excitatory synaptic strength are distributedaccording to a long-tailed distribution, typically the log-normal distribution. We show that weak synapses retainthe average membrane potential the UP-state. Only whenmembrane potential is in the UP state, a few very strongsynapses precisely transmit information about both rateand timing of the spike trains. Thus, our model also ac-counts for precisely-timed spike sequences reported in ex-periments. We will provide possible information processingof cortical neurons inferred from the precise informationtransmission based on the network structure.
Jun-nosuke [email protected]
MS100
Synthesizing and Simplifying Biological Networksfrom Pathway Level Information
Cellular networks involve a complex ”wireless” interac-tion propagating siganls between individual componentssuch as DNAs, RNAs and smaller molecules. Recent (andsometimes not-so-recent) surge of interest in investiga-tion of these networks have resulted in fascinating inter-
196 DS11 Abstracts
disciplinary collaborations between several disciplines suchas biology, control theory, mathematics and computer sci-ence. In this talk, I will summarize the research works thatmy collaborators and myself have been doing in the lastfew years in this area. We will discuss about synthesizingand simplifying networks from double-causal experimen-tal data, reverse engineering such networks via modular-response-analysis approach or from time-series data andmodular decomposition of such networks into simpler net-works. We will present the relevant biological background,explain the dynamic processes (models) that may arise, dis-cuss combinatorial and graph-theoretic algorithmic ques-tions that arise out of designing experimental protocols oroptimizing such networks and present computational re-sults. Minimal prior knowledge in control theory or com-binatorial algorithms will be assumed. The results dis-cussed are prior or ongoing joint research works with oneor more of the following collaborators (listed in alphabet-ical order): Reka Albert, Piotr Berman, German Enciso,Sema Kachalo, Paola Vera-Licona, Eduardo Sontag, KellyWestbrooks, Alexander Zelikovsky and Ranran Zhang.
Bhaskar DasGuptaDepartment of Computer ScienceUniversity of Illinois at [email protected]
MS100
Decomposition of Biological Networks
The key to uncovering functional and dynamical proper-ties of biochemical networks lies in their structural prop-erties. Our aim is to present a methodology that helps toextract information on dynamical properties of a complexbiochemical network that originates from the structure ofthe network itself.
Alice HubenkoUCSBDepartment of Mechanical [email protected]
Igor MezicUniversity of California, Santa [email protected]
MS100
Protein Kinase Target Discovery from Genome-wide mRNA Expression Profiling
By integrating ChIP-seq experiments, protein-protein in-teractions (PPIs), and kinase-substrate reactions, we canidentify kinases and transcription factors for functional val-idation based on genome-wide gene expression data. Theidea is to infer the most likely transcription factors thatregulate the changes in gene-expression; then use PPIs toconnect the identified factors to build transcriptional com-plexes; then use kinase-substrate reactions to rank kinasesthat most likely regulate the formation of the identifiedcomplexes.
Avi Ma’ayanDepartment of Pharmacology & Systems TherapeuticsMount Sinai School of [email protected]
MS100
Coarse-Graining Dynamics of (and On) Networks
In dynamical systems that involve networks, coarse-graining approaches are essential in helping us understandthe interplay between the structure and the dynamics ofnetworks. In this work, we propose and implement twodifferent coarse-graining approaches for reducing dynami-cal network problems. To illustrate these approaches, weconsider two dynamical network examples involving dis-tinct types of network dynamics: “dynamics of a network”and “dynamics on a static network”.
Yannis KevrekidisDept. of Chemical EngineeringPrinceton [email protected]
Karthikeyan Rajendran, Andreas TsoumanisPrinceton [email protected], [email protected]
Constantinos SiettosNational Technical University, Athens, [email protected]
MS101
Phase Space Method for Target Identification
Chaotic signals are very sensitive to the effects of filtering.In radar or sonar, scattering from a target is a linear pro-cess that may be described as a filter. The interaction of achaotic signal with a target produces a characteristic dis-tribution of neighbors in phase space which may be usedto identify the target. The particular distribution of pointsdepends on the rate of compression for the chaotic signaland on the target characteristics.
Thomas L. CarrollNaval Reseach [email protected]
MS101
Matched Filter for Chaos Radar
We describe a new approach to random-signal radar basedon the recent discovery of analytically solvable chaotic os-cillators. These surprising nonlinear systems generate ran-dom, aperiodic waveforms that offer an exact analytic rep-resentation and allow implementation of simple matchedfilters for coherent reception. Notably, this approach en-ables nearly optimal detection of noise-like waveforms with-out need for expensive variable delay lines to store wide-band waveforms for correlation. Mathematically, the wave-form is expressed as a linear convolution of a bit sequencewith a fixed basis function. We realize a simple matchedfilter for the waveform using a linear filter whose impulseresponse is the time reverse of the basis function. Impor-tantly, linear filters matched to multiple-bit sequences canbe defined, enabling pulse compression and spread spec-trum radar. We present an example oscillator, its matchedfilter, and corresponding simulation results demonstratingthe pulse compression radar concept. Preliminary exper-imental results using electronic circuits are also reported.
Ned J. CorronU.S. Army [email protected]
DS11 Abstracts 197
Jonathan N. BlakelyUS Army [email protected]
Mark StahlU.S. Army [email protected]
MS101
Acoustic Experiments with Multiple Chaotic Sig-nal Sources
The use of multiple chaotic sources for radar creates aunique spatial pattern that may be used to identify anobjects location without scanning a beam over differentangles. We report numerical and acoustic experiments us-ing 2 chaotic sources.
Frederic RachfordNaval Reserach LaboratoryMaterial [email protected]
MS101
De-Synchronized Chaos Angle Selective RadiationSystems
Temporal characteristics of electromagnetic systems arenot usually angle specific in radar/communication appli-cations; one exception is impulse radiation. Shown hereis a lesser known method in obtaining angle based selec-tivity using two or more ”de-synchronized” chaos (DSC)oscillators. DSC oscillators are ’epsilon equivalent’ with ashared periodic drive from which a temporal angle selectiveradiation pattern occurs. We discuss general applicationsof this angle selective chaos noise and then specifically astationary SAR application.
Jay WilsonComtech AeroAstro, IncLittleton, [email protected]
Bryan JamesComtech AeroAstro, [email protected]
MS102
Spike-time Dependent Coding and Noisy Ku-ramoto Networks
Neurons are sensitiveto their input firing rate through long-term potentiationor depression (spike-timing-dependent plasticity, STDP).Does STDP underlie the emergence/annihilation of syn-chronization? Using the Kuramoto-network, STDP is in-troduced by letting the coupling depend on the degree ofsynchrony: if synchrony increases, then the coupling dropsand vice versa. This yields oscillations of synchrony pre-suming STDP can be eliminated adiabatically. Despite itssimplicity the model provides a proper understanding ofalternating neural synchronization.
Andreas DaffertshoferResearch Institute MOVEVU University [email protected]
MS102
Revisiting Stochastic Differential Equation Modelsfor Ion Channel Noise in Hodgkin-Huxley Neurons
Channel noise in neurons can be modeled using continuous-time Markov chains nonlinearly coupled to a differentialequation for voltage, but there is interest in approximatingthese models with stochastic differential equations (SDEs).We analyzed three SDE models that have been proposed asapproximations to the Markov chain model and found thata channel-based approach can capture the distribution ofchannel noise and its effect on spiking in a Hodgkin-Huxleyneuron model, but subunit-based approaches cannot.
Joshua Goldwyn, Nikita Imennov, Michael FamulareUniversity of [email protected], [email protected],[email protected]
Eric Shea-BrownDepartment of Applied MathematicsUniversity of [email protected]
MS102
Network Effects of Noisy Synaptic Release
Synapses in the central nervous system can be extremelystochastic, with successful release rates per depolarizationas low as 20%. This introduces noise into single neuronresponse and neural networks, noise which is non-triviallycorrelated with network activity. In this talk, we modelthe release process and investigate how fluctuations canlead to interesting dynamical consequences. Results in-clude changes in neuronal gain of neurons, in firing vari-ability and in altered response to oscillatory input.
Herbert LevineUniv. of Cal. at San DiegoDepartment of [email protected]
MS102
Stochastic Synchrony in Networks With and With-out Feedback, Elucidation of the Rate of Conver-gence to Steady State in Type I and Type II Oscil-lators
Recently it was proposed that synchrony in the activityof mitral cells in the olfactory bulb could be mediatedby a stochastic synchronization mechanism. Synchronyin the olfactory bulb has been shown to develop slowly(≈ 150ms) unlike a PING-like mechanism. Here we inves-tigate the rate of convergence of stochastic synchrony ontothe steady-state probability density and compare theoreti-cal predictions with numerically calculated eigenvalues fora network of mitral and granule cells.
Sashi MarellaUniversity of PittsburghCenter for [email protected]
Bard ErmentroutUniversity of PittsburghDepartment of [email protected]
198 DS11 Abstracts
MS103
Geometry and Topology of Computer Dynamics
The realization that computers are nonlinear dynamicalsystems leads to a need for dynamical tools that can beapplied to unconventional data. The computer systems wehave studied appear to be of surprisingly low dimension.However, the data sets are quite noisy and—due to the timescales involved in computing—sparsely sampled, albeit es-sentially unlimited in length. We investigate dynamicalanalysis methods that extract state-space geometry andtopology from computer performance data.
Zachary AlexanderUniversity of ColoradoDepartment of Applied [email protected]
Amer DiwanUniversity of Colorado, [email protected]
James D. MeissUniversity of ColoradoDept of Applied [email protected]
Elizabeth BradleyUniversity of ColoradoDepartment of Computer [email protected]
MS103
The Dynamics of Granular Materials
We will present a novel approach to study force chain struc-tures of dense particulate systems. Our approach deploysalgebraic topology techniques which allow us to distinguishbetween the systems exposed to shear and compression.We use our method to compare experimental and theoreti-cal results in a well defined manner. The topological mea-sures can be also used to understand the dynamic featuresof the system and correlate these measures to phenomenasuch as jamming.
Miroslav KramarRutgers UniversityDepartment of [email protected]
Lou KondicDepartment of Mathematical Sciences, NJITUniversity Heights, Newark, NJ [email protected]
Konstantin MischaikowDepartment of MathematicsRutgers, The State University of New [email protected]
MS103
Experimental Determination of the Homology ofInvariant Manifolds
A useful, and under-exploited, source of information on ex-perimental dynamical systems is their transient behaviour.Transient trajectories explore the phase space near attrac-tors and can, for example, provide information about non-
attracting invariant sets such as repellers or saddles. Herewe analyse time series data from a system near to a period-doubling bifurcation and extract homological invariantsfrom a certain non-attracting invariant manifold associatedwith the limit cycle.
Mark Muldoon, Jeremy Huke, David BroomheadSchool of MathematicsUniversity of [email protected],[email protected],[email protected]
MS103
The Dynamics of Computer Behavior
I present a nonlinear-dynamics based framework for mod-elling, analyzing, and understanding the complex nonlineardynamics of modern computer systems. These dynamics—which are surprisingly low dimensional and often chaotic—depend on both hardware and software. This has im-portant implications in the computer systems community,which relies on mathematics that assumes linearity and ig-nores dynamics. I will demonstrate how the failure of theseassumptions affects the design tools used by hardware andsoftware architects.
Todd D. MytkowiczRiSEMicrosoft [email protected]
MS104
Spatially Localized Turbulence Structures in Tran-sitional Rectangular-duct Flow
We perform simulations of transitional rectangular-ductflow to investigate spatially localized turbulence structures.These structures depend on the aspect ratio A. At marginalReynolds numbers a puff is observed around A=1. As Aincreases the puff extends in the spanwise direction to oc-cupy the whole duct. Beyond A=4 a turbulent spot ap-pears. An oblique band, also observed in plane channels,arises at higher Reynolds numbers in spite of the presenceof side walls for A¿4.
Genta KawaharaDepartment of Mechanical ScienceOsaka [email protected]
Hiroki WakabayashiOsaka [email protected]
Markus UhlmannKarlsruhe Institute of [email protected]
Alfredo [email protected]
MS104
From Swift-Hohenberg to Navier-Stokes: Homo-clinic Snaking in Plane Couette Flow
For shear flows exact coherent solutions of the Navier-
DS11 Abstracts 199
Stokes equations play key roles in the transition to turbu-lence and the turbulent dynamics itself. Here we examinea new class of spatially localized solutions to plane Couetteflow. These solutions exhibit a sequence of saddle-node bi-furcations similar to the “homoclinic snaking’ phenomenonobserved in the Swift-Hohenberg equation. The localizedsolutions exist over a wide range of Reynolds numbers andbifurcate off the known spatially periodic states.
Tobias SchneiderHarvard [email protected]
John GibsonUniversity of New [email protected]
John BurkeBoston [email protected]
MS104
On the Edge of Turbulent Pipe Flow
The theoretical modelling of turbulence has advancedrapidly since the discovery of (spatially periodic) travelling-wave solutions. Relaxing periodicity in the streamwise di-rection, no localised ‘exact’ solutions are yet known. Weshow that states on the laminar-turbulent boundary are lo-calised, even at flow rates many times that of transitionalflow. We discuss the search for localised solutions in pipeflow, and examine the path of trajectories to and from theboundary-attractor.
Ashley WillisUniversity of [email protected]
Yohann DuguetLIMSI-CNRS, Orsay, [email protected]
Rich KerswellDepartment of MathematicsUniversity of Bristol, [email protected]
Chris PringleSchool of Maths and StatsUniversity of [email protected]
MS104
A Homoclinic Tangle on the Edge of Couette Tur-bulence
The ”edge state” hypothesis asserts that simple solutionslike periodic orbits mediate between laminar and turbulentshear flow. The stable manifold of an edge state separatesthese phases. The global structure of the separatrix, how-ever, is unknown. We show the existence of a homoclinicto a time-periodic edge state in Couette turbulence, im-plying a complex geometry of the separating manifold. Wefind important differences between the flow along the ho-moclinic and the conventional regeneration cycle.
Lennaert van VeenUOIT
Genta KawaharaDepartment of Mechanical ScienceOsaka [email protected]
MS105
Reduced Nonlinear Models of Internal Waves
Abstract not available at time of publication.
Roberto CamassaUniversity of North [email protected]
MS105
Internal Waves in the Ocean - Observations, The-ory and DNS
Spectral energy density of internal waves in the ocean ex-hibit a surprising degree of universality - it is given bythe Garrett and Munk Spectrum of internal waves, dis-covered over 30 years ago. I will explain that situation ismuch more interesting, and will describe recent theoreticaladvances in understanding internal waves. I will demon-strate that when using traditional wave turbulence theoryone runs to internal logical contradictions: the results ofthe theory (strong nonlinearity) contradict the underlyingassumptions (weak nonlinearity) used to build the theory.I will demonstrate possible directions out of the puzzle andwill elaborate on open questions and challenges.
Yuri V. LvovRensselaer Polytechnic [email protected]
MS105
Generation of Shear Flows by Three-wave Interac-tions in Stratified Flows
Stratified flow is investigated under the influence of large-scale, unbalanced forcing. In addition to the Boussinesqsystem, we study a model including only three-wave inter-actions. We demonstrate that three-wave interactions areresponsible for the generation of vertically sheared horizon-tal flows (VSHF), and that the VSHF flow component isthe most sensitive to resolution. Triple-wave interactionsplay a significant role in the distribution of wave energy,which does not exhibit asymptotic scaling for moderateFroude numbers.
Leslie SmithMathematics and Engineering PhysicsUniversity of Wisconsin, [email protected]
MS106
Effects of Coupling on Sensory Hair Bundles
Auditory signal detection relies on amplification to boostsound-induced vibrations within the inner ear. Activemotility of sensory hair-cell bundles has been suggestedto constitute a decisive component of this amplifier. Theresponsiveness of a single hair bundle to periodic stimu-lation, however, is limited by intrinsic fluctuations. Wepresent theoretical and experimental results showing thatelastic coupling of sensory hair bundles can enhance their
200 DS11 Abstracts
sensitivity and frequency selectivity by an effective noisereduction.
Kai DierkesMax Planck Institut fur Physik komplexer [email protected]
Jeremie BarralInstitut Curie, [email protected]
Benjamin LindnerMax Planck Institute for the Physics of Complex Systems,[email protected]
Pascal MartinInstitut Curie, [email protected]
Frank JulicherMax-Planck-Institut fur Physik komplexer [email protected]
MS106
The Effect of Tectorial Membrane and BasilarMembrane Longitudinal Coupling in Cochlear Me-chanics
In the classical theory of cochlear mechanics, structurallongitudinal coupling is neglected. Motivated by re-cent experimental observations, we introduce basilar mem-brane and tectorial membrane longitudinal coupling in amechanical-electrical-acoustical model of the cochlea thatincludes a micromechanical model for the organ of Cortiand feedback from outer hair cell somatic motility. Struc-tural longitudinal coupling broadens the frequency re-sponse of the basilar membrane, shortens its impulse re-sponse and stabilizes the active model of the cochlea.
Julien Meaud, Karl GroshUniversity of [email protected], [email protected]
MS106
A Cochlear Model Using the Time-averaged La-grangian and the Push-pull Mechanism in the Or-gan of Corti
Direct computation of for a cochlear model with viscousfluid remains a challenge. However, the ’WKB’ asymp-totic method works well. Particularly, the time-averagedLagrangean of Whitham provides the slowly varying ampli-tude function. This is extended for including viscous fluid.The geometry of the organ of Corti motivates the activepush-pull approximation for the cells which provide an ac-tive system of distributed sensors and actuators. Currentapplication is on mutant mice.
Charles SteeleStanford UniversityDept. Mechanical [email protected]
Sunil PuriaStanford UnversityDepts Mechanical Engineering, [email protected]
John OghalaiDepartment of OtolaryngologyStanford [email protected]
MS106
Dynamic Properties of Human Cochlear Process-ing Investigated with Otoacoustic Emissions
Click-evoked otoacoustic emissions (CEOAEs) are echoesto clicks that can be recorded in the ear canal. They areproduced in the inner ear (i.e., cochlea) as a by-productof the nonlinear gain mechanism responsible for compres-sion in hearing. The relation between dynamic features ofCEOAEs and time-dependent properties of the underlyingcochlear gain mechanism was investigated with the purposeof understanding how the intact hearing system processesonsets of sounds (0-10 ms).
Sarah Verhulst, James Harte, Torsten DauTechnical University of [email protected], [email protected],[email protected]
MS107
Computing the Boundary of Analyticity of Familiesof Quasi-periodic Solutions
We formulate and justify rigorously a numerically efficientcriterion for the computation of the analyticity breakdownof quasi-periodic solutions in Symplectic maps and 1-D Sta-tistical Mechanics models. Depending on the physical in-terpretation of the model, the analyticity breakdown maycorrespond to the onset of mobility of dislocations, or ofspin waves (in the 1-D models) and to the onset of globaltransport in symplectic twist maps. The criterion we pro-pose here is based on the blow-up of Sobolev norms ofthe hull functions. The justification of the criterion sug-gests fast numerical algorithms that we have implementedin several examples.
Renato CallejaDepartment of Mathematics and StatisticsMcGill [email protected]
Rafael de La LlaveUniversity of TexasDepartment of [email protected]
MS107
Arnold Diffusion Along a Chain of Oscillators
A chain of pendula connected by nearest neighbor couplingis a near–integrable system if the coupling is weak. Asa consequence of KAM, for most initial data the energyof each pendulum stays near its initial value for all time.We show that these KAM motions coexist with “diffusing”motions for which the energy can leak from any pendulumto any other pendulum, and it can do so with a prescribeditinerary. This is joint work with Vadim Kaloshin.
Mark LeviDepartment of MathematicsPennsylvania State [email protected]
DS11 Abstracts 201
MS107
Aubry-Mather Theory and Ghost Circles
I will explain the construction of ghost circles for mono-tone recurrence relations on more-dimensional lattices, forexample the Frenkel-Kontorova crystal model. Ghost cir-cles are gradient-flow invariant interpolations of an Aubry-Mather set of a particular rotation vector. In the case thatthe set of global minimizers in the ghost circle has a gap,there are non-globally minimizing stationary solutions ofthe gradient flow in the gaps.
Blaz MramorVU University [email protected]
Bob RinkDepartment of MathematicsFree University of [email protected]
MS107
Weak KAM Theory and Viscosity Solutions ofHamilton-Jacobi Equations
In this talk, I will give an introduction of the connec-tion between Aubry-Mather theory and several nonlinearPDEs, such as a Hamilton-Jacobi equation arising fromHomogenization theory and Aronsson equations from L-infinity variational problems. If time permits, I will alsotalk about recent joint work with Gomes, Iturriaga andSanchez-Morgado, in which we identified the Mather mea-sure selected by a variational scheme proposed by Evans.
Yifeng YuUniversity of [email protected]
MS108
Predicting Infectious Disease Extinction
Eradication of infectious diseases is an important goal forpublic health. In general, disease extinction occurs for fi-nite populations in finite time due to stochastic interactionsamong individuals. The theory of large fluctuations pre-dicts extinction to occur along a most probable trajectory,or optimal path. The time to extinction is proportionalto the probability of crossing the path. I will discuss theoptimal path to extinction for some single and multistraindisease models.
Simone BiancoUC, San [email protected]
Eric ForgostonMontclair State UniversityDept. of Mathematical [email protected]
Leah ShawThe College of William & [email protected]
Ira B. SchwartzNaval Research LaboratoryNonlinear Dynamical Systems Section
MS108
Stochastic Dynamics of Tumorigenesis
I will discuss a continuous-time birth-death process modelof tumorigenesis where mutations confer random additivefitness (birth rate) changes. We investigate the overallgrowth rate and diversity of the tumor in the asymptoticlimit, and the dependence of these features on parametersof the fitness landscape. Using experimental data, we ana-lyze this model at the time of patient diagnosis (i.e. totalpopulation reached size M) to study the generation of re-sistant populations in expanding populations of leukemicstem cells.
Jasmine FooHarvard [email protected]
Rick DurrettDuke [email protected]
Kevin LederHarvard [email protected]
John MayberryUniversity of the [email protected]
Franziska MichorHarvard [email protected]
MS108
The Effects of Stochasticity in the Dynamics ofMulti-Strain Diseases
We study the dynamics of multi-strain diseases, such asdengue and SARS, that display complex spatio-temporalbehavior resulting from the coupling introduced by the hostimmune response. This complex temporal evolution fre-quently results in recurrent excursions into regimes wherestochastic effects dominate. In this work we study the ef-fects of stochasticity on the dynamics of multi-strain dis-eases with latent period and cross-immunity, focusing inparticular on events that lead to disease extinction.
Luis Mier-y-Teran, Derek CummingsJohns Hopkins Bloomberg School of Public [email protected], [email protected]
MS108
Stochastic Extinction in Non-Gaussian Environ-ments with Differential Delay
Extinction processes are stochastic events that occur inapplications of finite populations, such as epidemics andchemical reactions. Nonlinear interactions typically leadto non-Gaussian noise sources. We consider the problemof stochastic extinction as a rare event occurring in sys-tems with delayed feedback and driven by non-Gaussiannoise. Using Melnikov perturbation theory, we show howdelay modulates non-power law behavior of mean times to
202 DS11 Abstracts
extinction in systems driven by non-Gaussian noise.
Ira B. SchwartzNaval Research LaboratoryNonlinear Dynamical Systems [email protected]
Lora BillingsMontclair State UniversityDept. of Mathematical [email protected]
Thomas W. CarrSouthern Methodist UniversityDepartment of [email protected]
Mark I. DykmanDepartment of Physics and AstronomyMichigan State [email protected]
MS109
Reachability Analysis of Idea Propagation on Net-works with Community Structure
This presentation formulates prediction questions in termsof reachability assessments computing the likelihood thatthe dynamics of interest will enter user-specified regions ofthe systems state space and applies the methodology toidea propagation on realistic social networks. Reachabilityis assessed by defining and solving appropriate semidefi-nite programs using sums-of-squares decomposition. Themethodology is applied to the propagation of Feynmandiagrams across physics communities and the geographicspread of the Swedish Social Democratic Party.
Michael BencomoNew Mexico [email protected]
MS109
Predictability of Social Network Dynamics: AnAppraisal
Enormous resources are devoted to the task of predictingthe outcomes of social network dynamics in a wide range ofdomains, but the quality of such predictions is often poor.Recently, important advances in network theory and dra-matic increases in availability of social dynamics data arebeing combined to enable significant progress in exploringand exploiting the predictability of social processes. Thispresentation reviews this progress and introduces the re-maining three talks of the minisymposium.
Richard ColbaughNew Mexico [email protected]
Kristin GlassNew Mexico [email protected]
MS109
Sentiment-Over-Time Analysis of Tweets
Microblogging, Twitter in particular, has become a preva-
lent medium for people to express their beliefs and feelings.As it has increased in popularity, researchers are focusingon its content. This paper will look at the results of usinga semi-supervised sentiment classifier to measure how pop-ular sentiment changes over time for various topics. Topicsare both specifically chosen as well as discovered using un-supervised topic classifiers.
Alexander D. GeorgeNew Mexico [email protected]
MS109
Ex-ante Prediction of Cascade Sizes on Networksof Agents Facing Binary Outcomes
A wide range of social, economic and popular cultural pro-cesses can be characterized as involving binary choice withexternalities (Schelling 1973). Agents have a choice be-tween two alternatives, and the payoff of an individual isan explicit function of the actions of others. We presentresults on ex ante predictability of cascade size on random,small world and scale free networks with minimal infor-mation on the connectivity and persuadability of a smallnumber of agents.
Paul OrmerodVolterra Consulting, [email protected]
Ellie CooperVolterra [email protected]
MS110
Spontaneous Formation and Evolution of the Chan-nel Network Inside Physarum Polycephalum Sheet-like Structures: Direct Experimental Observations
In the network evolution of Physarum polycephalum, animportant question concerns the initial stages of vein for-mation, which occur mainly at the advancing front. Wefocus on this question, with the aim to provide experimen-tal data allowing elaboration and tests of models of channelformation. Using infrared microscopy, and fluctuation anl-ysis, we show in particular that the structural developmentof channels occurs very early during the process. Velocime-try profiles of the fluids will be also presented.
Serge Bielawski
PhLAM/Universite Lille I,[email protected]
Paul DelyLab PhLAM/Universite Lille [email protected]
Christophe SzwajUniversite de Lille (France)Laboratoire [email protected]
Eric LacotLab. SpectroUJF-Grenoble (France)[email protected]
DS11 Abstracts 203
Olivier HugonSPECTROUniversite J. Fourier, Grenoble (France)[email protected]
Toshiyuki NakagakiThe School of Systems Information [email protected]
MS110
Channeling Instabilities in the Cytoplasm of Amoe-boid Cells
Physarum polycephalum exhibits periodic shuttle stream-ing through a network of tubular structures reaching ve-locities up to 1 mm/s. When the organism is small (<100 microns) there is no streaming. As it gets larger, flowchannels develop and streaming begins. We use a mul-tiphase flow model and discuss instabilities that produceflow channels within the gel. We present a simple modelof the flow-sensitive rheology of cytoplasm and discuss itssignificance for biological function.
Robert D. GuyMathematics DepartmentUniversity of California [email protected]
Toshiyuki NakagakiThe School of Systems Information [email protected]
Grady B. WrightDepartment of MathematicsBoise State University, Boise [email protected]
MS110
Transport and Mixing of Cytosol Through theWhole Body of Physarum Plasmodium
We study the net transport and mixing of chemicals inthe true slime mold Physarum polycephalum. The shuttlestreaming of the amoeba is characterized by a rhythmicflow in which the protoplasm streams back and forth. Weformulate a simplified model to consider the mechanism bywhich net transport can be induced by shuttle (or periodic)motion inside the amoeba. We discuss the effects of thesectional boundary motion on the net transport.
Makoto IimaResearch Institute for Electronic ScienceHokkaido [email protected]
Toshiyuki NakagakiThe School of Systems Information [email protected]
MS110
Mechanics of Amoeboid Locomotion Driven byContraction Waves and Friction Control
Crawling by amoeboid movement is a fundamental form ofbiological locomotion. In this report, we considered rheo-logical mechanics for the crawling driven by propagation ofcontraction wave along slender body. We proposed a the-oretically tractable model. A message from the modeling
is that not only speed and but also direction of locomotiondepended on the timing of active anchoring on the ground.A mechanism in the amoeboid crawling is shown.
Toshiyuki NakagakiThe School of Systems Information [email protected]
Yoshimi TanakaThe School of Systems Information ScienceFuture University [email protected]
MS111
Extreme Events: The Larger, the Better Pre-dictable
We investigate the predictability of extreme events in timeseries. Common examples for extreme events are natu-ral hazards such as earthquakes, strong precipitation orstrong turbulent wind gusts. We focus on the question, un-der which circumstances large events are better predictablethan smaller events. Therefore we use a simple predictionalgorithm, and study its performance for the prediction ofincrements and threshold crossings in stochastic processes,wind speed recordings and time series generated from en-semble weather forecasts. Although our approach is simple,it allows us to understand effects which are observed for theprediction of strong wind gusts, long jumps in moleculardiffusion and solar electric particle events.
Sarah HallerbergTU ChemnitzChemnitz, [email protected]
MS111
A Mathematical Framework for Critical Transi-tions
Critical transitions, or tipping points, have been encoun-tered in a wide variety of applications including climatemodeling, ecology and medicine. A critical transition is arapid qualitative change away from a stable regime. Themajor goal is to predict these transitions from time seriesdata. We formalize critical transitions mathematically us-ing stochastic multi-scale dynamical systems. Furthermorewe present analytical and numerical results on the predic-tion of critical transitions for normal form models.
Christian KuehnCenter for Applied MathematicsCornell [email protected]
MS111
Potential Analysis of Geophysical Time Series
We apply the method of potential analysis comprisingderivation of the number of climate states and system po-tential coefficients. Patterns of potential analysis indicatepossible bifurcations and transitions. The method is testedon artificial data and applied to climatic records [Livina etal, Clim Past 2010]. An application of the method in amodel of globally coupled bistable systems [Vaz Martins etal, PRE 2010] confirms its applicability for studying timeseries in statistical physics.
Valerie Livina
204 DS11 Abstracts
University of East AngliaNorwich, [email protected]
MS111
Transition to Instability in Financial Markets withMany Heterogeneous Agents
We model a financial market as a place where infinitelymany agents trade a risky asset. Each agent forms expec-tations about the future development of the asset’s priceby picking one of a number of available forecasting rules.All agents use the same evaluation criterion, but they suf-fer from an idiosyncratic bias; consequently, the agents aredistributed over the forecasting rules. Based on their fore-casts, agents submit a demand schedule, from which themarket price of the risky asset is determined. As the newprice is revealed, the evaluation criteria and the agentschoices of forecasting rules are updated. The price dy-namics is thus described by a low order dynamical system.Typically, if either the idiosyncratic bias or the risk aver-sion of the agents decrease, the fundamental equilibrium ofthe system destabilises: this has negative implications forthe total welfare of the market participants. Recently ithas been shown that, contrarily to the common opinion ofeconomists and policy makers, the same occurs if deriva-tive securities are added to the market, and that in thiscase the negative welfare effects can be disastrous.
Florian Wagener
University of Amsterdam (CeNDEF)Amsterdam, [email protected]
MS112
The Lagrangian Description of Aperiodic Flows:New Concepts and Tools
New Lagrangian tools are introduced which are success-ful in achieving a detailed description of purely advec-tive transport events in general aperiodic geophysical flows.First is discussed the concept of Distinguished Trajectorywhich generalizes the concept of fixed point for aperiodicdynamical systems. It is built on a function that detectssimultaneously, invariant manifolds, hyperbolic and non-hyperbolic flow regions, thus insinuating the active trans-port routes in the flow. Once these are recognized, thetransport description is completed by means of the directcomputation of the stable and unstable manifolds of theDHTs.
Ana M. ManchoInstituto de Ciencias MatematicasConsejo Superior Investigaciones [email protected]
MS112
Transport in Time-Dependent Flows – AnOverview
Transport theory seeks to quantify flux between regions inphase space. Traditional methods are based on construct-ing partial barriers containing lobes; these are naturallyformed formed from heteroclinic intersections between in-variant manifolds. Aperiodically time-dependent dynami-cal systems may have no hyperbolic invariant sets, and sonew ideas must be developed. We will give a short reviewof methods based on short time information using Lya-
punov exponents, distinguished trajectories, approximateinvariant sets, and transitory dynamics.
James D. MeissUniversity of ColoradoDept of Applied [email protected]
MS112
Set-oriented Numerical Analysis ofTime-dependent Transport
The numerical analysis of transport processes is central forunderstanding the macroscopic behavior of classical dy-namical systems as well as time-dependent systems suchas fluid flows. We review different theoretical concepts andtheir numerical implementation into a set-oriented frame-work. We demonstrate that the geometric approach basedon invariant manifolds and Lagrangian coherent structuresand the probabilistic concept which relies on transfer op-erators give consistent results. Finally, potential combina-tions of these techniques are discussed.
Kathrin Padberg-GehleInstitute of Scientific ComputingTU [email protected]
Gary FroylandUniversity of New South [email protected]
MS112
Lagrangian Transport Phenomena in 3D LaminarMixing Flows
Mixing in 3D laminar flows is key to many industrial sys-tems. Examples range from the traditional viscous mix-ing via compact processing equipment down to emergingmicro-fluidics applications. Central question is “How toachieve efficient mixing?” Mixing by fluid motion only de-fines an important subclass and is determined geomet-rically through coherent structures formed by the La-grangian fluid trajectories. Such formation and its im-pact upon 3D transport is demonstrated by way of twoexperimentally-realisable flows.
Michel SpeetjensLaboratory for Energy Technology, Dept. Mech. Eng.Eindhoven University of [email protected]
MS113
Aggregation and Fragmentation of Inertial Parti-cles in Random Flows
We present a coupled model for advection, aggregation andfragmentation that is based on the dynamics of individual,inertial particles in three-dimensional random flows appliedto marine aggregates. We show that fragmentation is themost important process determining largely the obtainedsteady-state size distribution. We discuss how the size dis-tribution depends on the collision efficiency, the bindingstrength of the aggregates as well as the turbulence level.Furthermore we extend this approach to fractal aggregates.
Ulrike FeudelUniversity of [email protected]
DS11 Abstracts 205
MS113
Droplet Distributions in Binary Mixtures
We present experimental data for the evolution of thedroplet size distribution in a binary mixture where demix-ing is induced by a continuous temperature ramp. Oursystem serves as an example of demixing of multiphase flu-ids as encountered in many industrial and natural processeslike alloys, magmas and clouds. The precise control of theexperiment provides us with hitherto not accessible infor-mation on the mechanisms of droplet creation, growth andinteraction as well as their effects on the evolution of thedroplet size distribution.
Tobias LappMPI Dynamics and [email protected]
Martin RohloffMPI Dynamics and Self-Organization [email protected]
Juergen VollmerMPI Dynamics and Self [email protected]
Bjoern HofMPI Dynamics and Self-Organization [email protected]
MS113
Chaotic Motion of Inertial Particles in Finite Do-mains
The motion of inertial particles is investigated in a time-periodic flow in the presence of gravity. The flow is re-stricted to a finite (or semi-infinite) vertical column, andthe dynamics is therefore transiently chaotic. The longterm motion of the center of mass is a uniform settling. Thesettling velocity is found to differ from the one that wouldcharacterize a still fluid, and the distribution of an ensem-ble of settling particles spreads with a well-defined diffusioncoefficient. The underlying chaotic saddle appears to havea height-dependent fractal dimension. The coarse-graineddensity of both the natural measure and the conditionallyinvariant measure (defined along the unstable manifold) ofthe saddle is smooth, and exhibits a local maximum asa function of the height. The latter density correspondsto the eigenfunction of the first eigenvalue of an effectiveFokker–Planck equation subject to an absorbing boundarycondition at the bottom. The transport coefficients can bedetermined as averages taken with respect to the condi-tionally invariant measure.
Tamas TelInstitute for Theoretical PhysicsEtovos University, [email protected]
MS113
A Reactive-flow Model of Phase Separation inFluid Binary Mixtures with Continuously RampedTemperature
We revisit the phase separation of binary mixtures sub-jected to a sustained change of temperature from the pointof view of reactive flows. Exploiting this new perspective,we describe the demixing dynamics by a spatial model ofadvection-reaction-diffusion completed with nucleation and
coagulation of droplets. In this approach several featuresof the dynamics — in particular an oscillatory variation ofthe droplet density — become numerically and analyticallyaccessible. For instance, the model helps to clarify why theoscillation frequency is hardly affected by the flow. Froma more general perspective it provides valuable insight inthe droplet-growth dynamics of thunderstorm clouds.
Juergen VollmerMPI Dynamics and Self [email protected]
Izabella BenczikMPI Dynamics and [email protected]
Jan-Hendrik TrosemeierMPI Dynamics and Self-Organization [email protected]
MS114
Ultra-fast Physical Random Number Generationbased on Chaotic Photonic Integrated Circuits
Photonic integrated circuits that emit broadband chaoticoptical signals are employed as sources for ultra-fast gen-eration of true random bit sequences. Chaos dynamics insuch photonic devices emerge from internally built opticalcavities that suppress intrinsic periodicities, exhibit flat-tened broadband spectra and are completely controllable.After sampling, quantization and using most significantbits (MSB) elimination post-processing, truly random bitstreams with bit-rates as high as 140 Gb/s are generated.
Apostolos Argyris, Dimitris SyvridisDepartment of Informatics and TelecommunicationsNational & Kapodistrian University Of [email protected], [email protected]
MS114
Synchronization of Random Bit Generators Basedon Coupled Chaotic Lasers and Application toCryptography
Random bit generators (RBGs) constitute an essential toolin cryptography. The secure synchronization of two RBGs,however, over a public channel remains an open challenge.We propose a method, whereby two fast optical RBGscan be synchronized. Using information theoretic analysiswe demonstrate security against a powerful computationaleavesdropper, capable of noiseless amplification, even whenall system parameters are publicly known. The method isextended to secure synchronization of a small network ofRBGs.
Ido KanterDepartment of Physics,Bar Ilan University, [email protected]
Yitzhak PelegBar Ilan niversity, [email protected]
Meital Zigzag, Michael RosenbluhBar Ilan Ubiversity, [email protected], [email protected]
206 DS11 Abstracts
Wolfgang KinzelUniversity of Wuerzburg, [email protected]
MS114
12.5 Gb/s Random Number Generation Using Am-plified Spontaneous Emission
We describe our recent experiments to generate and testrandom numbers at high rates by using high-speed detec-tion of optical noise signals. Amplified spontaneous emis-sion, either in a fiber amplifier or in a superluminescentlight-emitting diode (SLED) is shown to be capable of gen-erating a large, easily detected fluctuating electrical signalthat can be exploited for random number generation. Wereport random bit generation at rates of up to 12.5 Gb/s,using only a single XOR postprocessing step to reduce cor-relations and bias.
Thomas E. MurphyUniversity of Maryland, College ParkDept. of Electrical and Computer [email protected]
Xiaowen LiBeijing Normal [email protected]
Caitlin R. S. Williams, Julia SalevanUniversity of MarylandDept. of [email protected], [email protected]
Rajarshi RoyUniversity of [email protected]
MS114
Physical Random Bit Generator with ChaoticLasers
Fast generation of non-deterministic random numbers is re-quired to improve the security of information and commu-nication systems. We review our recent progress on high-speed generation of good-quality random bit sequences us-ing fast chaotic semiconductor lasers. We have stablygenerated random bit sequences in real time by directlysampling the output of two chaotic semiconductor lasers.We have experimentally demonstrated the possibility offaster random bit generation using multi-bit samples ofbandwidth-enhanced chaos in coupled lasers.
Atsushi Uchida, Taiki Yamazaki, Yasuhiro AkizawaDepartment of Information and Computer SciencesSaitama [email protected],[email protected],[email protected]
Takahisa Harayama, Satoshi Sunada, KazuyukiYoshimura, Peter DavisNTT Communication Science LaboratoriesNTT [email protected],[email protected], [email protected],[email protected]
MS115
The Role of Transient Potassium Channels inPhase Resetting and Stochastic Synchrony in theOlfactory Bulb
Blockade of the A-type K-channel with 4-AP in mouse ol-factory mitral cells (MC) significantly reduces the peak ofthe empirically measured phase response curve, while MCstochastic synchrony is attenuated. These counterintuitiveresults indicate that removal of the inhibitory A-currentrenders MCs less capable of participating in correlation-driven population oscillations. A biophysically realistic cellmodel confirms the experimental findings and shows that ahomoclinic bifurcation may underly the dynamical mecha-nism.
Aushra AbouzeidDepartment of MathematicsUniversity of [email protected]
Anne-Marie M. OswaldDepartment of Biological SciencesCarnegie Mellon [email protected]
Roberto F. GalanCase Western Reserve UniversityDepartment of [email protected]
Nathan UrbanCarnegie Mellon [email protected]
Bard ErmentroutUniversity of PittsburghDepartment of [email protected]
MS115
Effects of the Frequency Dependence of Phase Re-sponse Curves on Network Synchronization
Spatiotemporal pattern formation in neuronal networks de-pends on the interplay between cellular and network syn-chronization properties. The PRC can serve as an indicatorof cellular propensity for synchronization. We investigatethe frequency modulation of PRCs and its effect on syn-chronization in large-scale excitatory networks. We findthat frequency-induced PRC attenuation affects networksynchronization in some cases and that these effects arerobust to different network structures, synaptic strengthsand modes of driving neuronal activity.
Christian G. FinkDept of PhysicsUniversity of [email protected]
Victoria BoothUniversity of MichiganDepts of Mathematics and [email protected]
Michal ZochowskiBiophysicsUniversity of [email protected]
DS11 Abstracts 207
MS115
Using PRC’s to Understand How Antiepilep-tic Drugs and Deep Brain Stimulation PreventSeizures
Epilepsy is a multi-scale disease where causes and treat-ments occur at the scale of ion channels but the diseasepresents as seizures at a cortical scale. We use phase re-sponse curves (PRCs) measured from neurons to under-stand how antiepileptic drugs affect neuronal dynamics.We then use the PRCs to predict how those changes affectnetwork synchrony to prevent seizures. Furthermore, wehave used PRCs to understand how deep brain stimulationmay prevent network synchrony.
Theoden I. NetoffUniversity of MinnesotaDepartment of Biomedical [email protected]
Bryce Beverlin II, Brendan MurphyUniversity of [email protected], [email protected]
Charles WilsonUniversity of Texas, San [email protected]
MS115
Isochrons and Phase Response in Multiple Time-Scale Systems
Intrinsic phase response properties shape how neurons in-teract in networks. We recently demonstrated how multipletime-scale dynamics shape phase response curves for burst-ing neurons, which rhythmically alternate between spikingand quiescence. Key to the analysis is the computationof isochrons, manifolds of points about a limit cycle whichhave the same asymptotic phase. Here we consider the re-lation of isochron geometries and phase response propertiesfor a range of spiking and bursting neuronal models.
Eric SherwoodBoston [email protected]
MS116
Spectral Stability of Shock Layers for DissipativeHyperbolic-parabolic Systems
This work focuses on the stability theory of nonlinear trav-eling waves, with an emphasis on front propagation arisingin continuum models of compressible flow. We report ona recent collection results that use both analytical and nu-merical techniques as part of a general strategy for provingthe stability of high Mach number viscous shock layers anddetonation waves. Our technical approach centers aroundEvans function computation, energy estimates, and asymp-totic ODE techniques.
Jeffrey HumpherysBrigham Young [email protected]
MS116
Existence, Stability and Dynamics of Some Single-and Multi-Component Solitary Waves: From The-
ory to Experiments
In this talk, we will present an overview of our recent the-oretical, numerical and experimental work on a “quartet”of coherent structures arising in dispersive wave equations:dark solitons in single-component NLS equations, dark-bright symbiotic states in two-component NLS models, vor-tices in two-dimensional, single-component analogs of thesemodels, and finally vortex-bright symbiotic states in two-component, two-dimensional models. We will focus on thebifurcations that lead to the emergence of such states, willdiscuss their spectral and dynamical stability and exam-ine their relevance to experiments in atomic and opticalphysics.
Panayotis KevrekidisUMass, [email protected]
MS116
Localized Standing Waves in InhomgeneousSchrodinger Equations
In this talk I will discuss the stability of some solitons aris-ing in models used to create a Bose-Einstein Condensate(BEC). BEC’s were first theorized by Bose and Einsteinas a state of matter occurring when a dilute bosonic gas iscooled very close to absolute zero. In such instances, quan-tum tangling occurs and macroscopic quantum effects canbe observed. The talk will outline how the Maslov indexand composite phase portrait techniques can be used to es-tablish the instability of standing waves to NLS equationswith an inhomogeneous nonlinear term. The geometric na-ture of the techniques used means that instability can beestablished by simple observations of the soliton’s orbit inthe phase plane. Then the talk will outline and establishthe instability of a family of gap solitons to a related set ofequations, again using Maslov index techniques.
Robert MarangellUNC Chapel [email protected]
Christopher JonesUniversity of North Carolina and University of [email protected]
Hadi SusantoThe University of NottinghamUnited [email protected]
MS116
Bifurcations of Travelling Waves in the OregonatorModel for the BZ Reaction
Travelling wave solutions of a reaction-diffusion systemmodelling the Belousov-Zhabotinsky reaction are studied.The model consists of two equations and contains four pa-rameters, two of them, the stoichiometry factor f and theexcitability parameter ε play important role in the exis-tence of travelling waves. First we present numerical re-sults concerning the existence of pulse type, so-called ox-idation travelling waves. The main feature is the saddle-node bifurcation in the solutions, giving upper bounds on ffor the existence of travelling waves. The values of the up-per bound fm of the stoichiometry factor f are determinedin terms of ε for various values of the kinetic parameter qand D, the ratio of the diffusion coefficients. Then other
208 DS11 Abstracts
types of travelling waves, reduction waves and wave trainsare studied numerically. Our aim is to divide the parame-ter space into regions according to the type and the numberof travelling waves.
Peter L. SimonInstitute of MathematicsEotvos Lorand [email protected]
MS117
Using the Structure of Inhibitory Networks to Un-ravel Mechanisms of Spatiotemporal Patterning
We established a relationship between an important struc-tural property of an inhibitory network, its colorings, andthe dynamics it constrains. Using a model of the insectantennal lobe we show that our description allows the ex-plicit identification of the groups of inhibitory interneuronsthat switch, during odor stimulation, between activity andquiescence. This description optimally matches the per-spective of the downstream neurons looking for synchronyin ensembles of presynaptic cells.
Collins AssisiUC [email protected]
Maxim BazhenovDepartment of Cell Biology and NeuroscienceUniversity of California, [email protected]
MS117
Modeling and Experiment on the Control of Reaf-ference During Locomotion
Resistance reflexes help stabilize posture against outsideperturbation. Resistance reflexes triggered by voluntarymovement can interfere with that movement. In verte-brates and some invertebrates, descending motor com-mands include excitation of inhibitory interneurons thatprevent unwanted reafference through primary afferent de-polarization. In crayfish, the coxo-basal chordotonal or-gan (CBCO) is a stretch receptor that spans the coxa-basipodite joint that enables the walking legs to move upand down. CBCO afferents mediate resistance reflexes tomaintain leg position during standing, but during walk-ing, those resistance are reversed to produce assistance re-flexes. To determine reflex reversal occurs during normalwalking, we have developed three approaches. We corre-late limb movements of freely behaving crayfish during re-flex responses and normal walking with EMG recordingsof the leg depressors (Dep), and the anterior and posteriorlevator (Lev) muscles obtained from implanted electrodes.We record from CBCO afferents, central neurons, and Depand Lev motorneurons (MNs) in an isolated nervous sys-tem that is connected to a computational neuromechanicalmodel of the crayfish thorax and leg to form a real-time,closed-loop hybrid system. Dep and Lev MN activity ex-cited model Dep and Lev muscles that move the model leg.The leg movement stretch and release the model CBCO;model CBCO length changes are transduced into identi-cal movements of live CBCO generating afferent responsesthat excite the CNS. We use this system to determine thedynamic changes in reflex loop gains it switches from resis-tance to assistance reflexes during the onset of locomotorCPG activity. We have developed a computational neu-romechanical model of a 4-legged crayfish, including all
relevant neurons, muscles, and CBCOs, that we place ina virtual underwater world and use to test whether theproposed circuit mechanisms can account for the animal’slocomotor and reflex behavior.
Donald EdwardsNeuroscience InstitudeGeorgia State [email protected]
Giselle Linan-VelezBiology DepartmentGeorgia State [email protected]
Eric RandallNeuroscience InstituteGeorgia State [email protected]
Daniel CattaertInstitut de Neurosciences Cognitives et Integrativesd’[email protected]
MS117
Duty Cycle as Order Parameter for Polyrhythms inMultifunctional Center Pattern Generator Motifs
We examine exact and phase- phenomenological modelsfor multifunctional Center Pattern Generators. A motifof three reciprocally inhibitory cells is shown to generatemultiple bursting rhythms. CPG polyrhythms and the cor-responding attractors are determined by the duty cycle ofbursting. Through the examination of the mappings forphase lag between the cells we reveal the organizing centersof emergent polyrhythmic patterns and their bifurcationsas the synaptic coupling asymmetry and the duty cycle arevaried.
Andrey ShilnikovNeuroscience Institute and Department of MathematicsGeorgia State [email protected]
Jeremy WojcikGeorgia State UniversityDept. Mathematics and [email protected]
Matt BrooksGeorgia State [email protected]
Robert ClewleyDepartment of Mathematics and StatisticsGeorgia State [email protected]
MS117
Maintaining Novel Inputs in a Working MemoryModel
We present a model that displays numerous properties as-sociated with working memory: It exhibits persistent activ-ity among a random subset of cells and, therefore, main-tains completely novel input patterns. Persistent statesare robust to distractors, the network switches activity if
DS11 Abstracts 209
presented with a more salient input pattern and neuronshave firing properties constrained by experimental data.Finally, we explore how changes in neuromodulators suchas dopamine may lead to neurological disease.
David H. TermanThe Ohio State UniversityDepartment of [email protected]
Robert McDougal, Kyle Lyman, Brian Myers, MustafaZekiOhio State [email protected], [email protected],[email protected], [email protected]
Chris FallDepartment of Anatomy and Cell BiologyUniversity of Illinois at [email protected]
MS118
Nonlinear Delayed Optical Phase Oscillator forHigh Performance Chaos Synchronization: Dy-namics and Chaos Communication at 10Gb/s
A key issue in secure optical chaos communications is thesynchronization quality of the receiver chaos, with theemitter chaos. Various nonlinear electro-optic delayed dy-namics have been proposed for the implementation of op-tical chaos communications, with the particularly attrac-tive features of a high quality chaos synchronization capa-bility, and a huge operational bandwidth. These uniquefeatures allowed recently for the demonstration of stateof the art results in terms of speed (> 10Gb/s) and dis-tance (> 100km). The study and the development of thewhole transmission system also led to the definition of anew class of delay dynamics, for which the nonlinear terminvolves two time delays, a long one, and a much shorterone which is introducing a so-called temporally nonlocalnonlinear delayed feedback. In this communication, wewill report on both the dynamical features observed forthis particular new class of delay dynamics, as well as onthe chaos communication setup and its related successfulfield experiments.
Laurent LargerUniversite de Franche-ComteFEMTO-ST institute / Optics [email protected]
Lavrov Roman, Maxime JacquotFEMTO-ST institute, Optics [email protected], [email protected]
Vladimir UdaltsovVavilov Optical State [email protected]
MS118
Estimating Model Parameters from Time Series byUsing Chaotic Synchronization and Speed-gradientMethodology
We present a new parameter estimation procedure for non-linear systems. It works by imposing the synchronizationbetween the system and the model which contains the pa-rameters whose values one wish to estimate, and it is based
on the speed-gradient (SG) methodology. It allows multi-parameter identification using as an input signal a scalartime series obtained from the nonlinear system. This pro-posed procedure allows us to derive sufficient conditionsfor synchronization and hence for proper parameter esti-mation.
Elbert E. MacauINPE - Brazilian National Institute for Space ResearchLAC - Laboratory for Computing and [email protected]
Ubiratan S. FreitasCORIAUniversite de [email protected]
MS118
Synchronization of Uncoupled Dynamical SystemsInduced by White and Colored Noise
We study the synchronization of uncoupled dynamical sys-tems due to a common noise source. In particular, weconsider two identical FitzHugh-Nagumo systems, whichdisplay both spiking and non-spiking behaviours in chaoticor periodic regimes. Synchronization is tested with bothwhite and coloured noise, showing that coloured noise ismore effective in inducing synchronization of the systems.We also study the effects on the synchronization of param-eter mismatches and of the presence of intrinsic noise.
Ines P. MarinoUniversidad Rey Juan CarlosMostoles, [email protected]
MS118
Competing Chaotic Synchrony: Theory and Exper-iment
This presentation will start with a quick introduction tothe minisymposium’s talks. Then the idea of competingsynchrony will be presented in the context of three linearlycoupled oscillators. The theory behind the mechanism ofcompeting synchrony will be discussed and a few practicalexamples like lasers, electronic circuits, wildlife populationsand neurons will be used for illustration.
Epaminondas RosaIllinois State UniversityDepartment of [email protected]
MS119
Oscillatory Dynamics of a Structured ConsumerResource Model
Previous investigations of structured consumer resourcemodels based on so-called renewal equations (de Roos,Diekmann and Metz, American Naturalist 1992) have beenhampered by a lack of appropriate numerical methods. Inparticular, it has not been possible to track periodic or-bits of the systems considered due to issues such as thepresence of discontinuities. Here we present results fromnumerical bifurcation studies which use new methods ableto deal with the delays and discontinuities present.
David A. Barton
210 DS11 Abstracts
University of Bristol, [email protected]
MS119
Invariant Tori in Scalar State-dependent DDEs
We demonstrate complex dynamics including bi-stability ofperiodic orbits, invariant tori, double Hopf bifurcations andperiod doubling in a very simple model problem consistingof a single scalar delay equation with two linearly state-dependent delays. We will use the model to illustrate thepossible dynamics of DDEs and the associated bifurcationstructures, and to introduce some of the issues which willbe addressed in the other presentations in this session.
Tony R. HumphriesMcGill UniversityMathematics & [email protected]
Renato CallejaDepartment of Mathematics and StatisticsMcGill [email protected]
MS119
Floquet Multipliers for Periodic Solutions of DelayEquations with Several Delays
Suppose that hi(x) is a step function satisfying hi(x) =hi(sgn(x)) for all x. Consider the following scalar delayequation with discontinuous feedback:
(1) y′(t) =
D∑i=1
hi(y(t − di)).
Given δ > 0, consider also
(2) x′(t) =
D∑i=1
fi(x(t − di)),
where the fi are smooth and satisfy fi(x) = hi(x) for |x| ≥δ. Periodic solutions p of (1) are often easy to compute.If p satisfies certain conditions, then for δ small enough(2) has a periodic solution q that is “similar”’ to p andwhose Floquet multipliers can be explicitly computed fromknowledge of the semiflow of (1) near p. We discuss thiscomputation, and what estimates we can retain on Floquetmultipliers if (2) is appropriately perturbed.
Benjamin KennedyGettysburg CollegeDepartment of [email protected]
MS119
Invariant Tori and Resonances for Time PeriodicDelay Differential Equations
We study the bifurcation of a class of time-periodic scalardelay differential equations. It is shown that at the criticalvalues of the parameters a Neimark-Sacker bifurcation ofthe period map takes place and an invariant torus appearsin an extended phase space. The local bifurcation analysiscan be performed by using a spectral projection method,center manifold reduction and normal forms. The existenceof the invariant torus further away from the critical value
is a difficult problem. Somewhat surprisingly, strong reso-nances of 1:4, 1:3 and 1:1 types may also occur, which leadto intriguing behaviors of the system.
Gergely RostBolyai Institute, University of [email protected]
MS120
Investigating Bacteria-immune Dynamics in Pre-mature Infants
Necrotizing enterocolitis (NEC) is a severe disease of thegastrointestinal tract in preterm infants, characterized byan impaired epithelium and exaggerated inflammatory re-sponse. Activation of epithelial Toll-like receptors initiatesa widespread inflammatory response that eliminates bac-teria but damages the epithelial barrier. A mathematicalmodel of bacteria-immune interactions within the intestineis used to analyze conditions in which inhibiting receptoractivation may reduce excessive inflammation and epithe-lial damage in NEC and thereby prevent bacterial tissueinvasion.
Julia ArcieroDepartment of MathematicsUniversity of [email protected]
Bard ErmentroutUniversity of PittsburghDepartment of [email protected]
Yoram VodovotzUniversity of PittsburghDepartment of [email protected]
Jonathan E. RubinUniversity of PittsburghDepartment of [email protected]
MS120
Non-Invasive Pathogen Pro-filing and New Prospects for In-Host Monitoringof Infection and Immune Response
In the laboratory setting it is straightforward to measurethe growth of micro-organisms in a wide variety of media,continuously or in batch. Very little appears to be knownconcerning the growth of organisms within a human host.We report data that show that an inexpensive, rapid andnon-invasive method exists to measure the number of cer-tain common pulmonary pathogens in ventilated patientsover time. The same method also provides informationconcerning the state of the patients innate and adaptiveimmune response. Our goal, described in this talk, is howto combine these data with a mathematical model to studythe process of pulmonary infection and ventilator associ-ated pneumonia.
Erik M. BoczkoDepartment of Biomedical InformaticsVanderbilt University Medical [email protected]
Todd Young
DS11 Abstracts 211
Ohio UniversityDepartment of [email protected]
Patrick Norris, Addison MayVanderbilt University Medical [email protected],[email protected]
MS120
Bacterial Infection: From theory to Experimentsand Back
Models describing bacteria- neutrophil (bacteria-eatingcells) interactions are constructed axiomatically and pro-vide a clinically important qualitative prediction: undernatural conditions the bacteria population is expected toexhibit bi-stability. Carefully designed experiments clearlydemonstrate that bi-stability indeed emerges and allow pa-rameterizing the proposed models. A parameterized modelis then utilized as a building block in more detailed modelsthat examine the in-vivo immune response under healthand various immunodeficiency conditions.
Roy Malka, Vered Rom-KedarThe Weizmann InstituteApplied Math & Computer [email protected],[email protected]
MS120
Delayed Immune Response to Plasmodium Infec-tion
Plasmodium infections exhibit intrahost oscillations. Weanalyze a deterministic model for such behavior with theadded feature that the immune effectors are stimulatedby the pathogens at a delayed time. Delays or time lagscan excite oscillations causing them to persist or becomechaotic. We examine two kinds of delays, constant andstate-dependent. We show how the latter can cause thebranch of periodic solutions to be either sub or supercriti-cal.
Jonathan MitchellHardin-Simmons UniversityDepartment of [email protected]
Thomas W. CarrSouthern Methodist UniversityDepartment of [email protected]
MS121
An Efficient Spatially-explicit Model of CardiacMyofilament Dynamics
Contraction of cardiac muscle involves binding of bothCa2+ and myosin crossbridges to sites on the actin fila-ments. Tropomyosin molecules in each thin filament spanstructurally link about twenty-six of these binding sites.We found that a Markov model of interacting sites repro-duced the dynamics of muscle contraction, and could bereduced to an efficient set of coupled ordinary differentialequations through the use of periodic boundary conditions
and the elimination of degenerate Markov states.
Stuart G. CampbellUniversity of [email protected]
Andrew D. McCullochDepartment of BioengineeringUniversity of California San [email protected]
Kenneth CampbellDepartment of Physiology and Center for Muscle BiologyUniversity of [email protected]
MS121
Overview of Multi-scale Modeling of Cardiac Con-traction
The hearts most important function is to serve as a me-chanical pump that circulates blood throughout the body.This function is a result of complex interactions betweenthree interdependent systems: voltage, calcium, and me-chanics. In this talk we will give an introduction to howcardiac contraction can be modeled and show some of thecomplex dynamics arising from the cross-talk between thethree systems as well as problems and unique challenges inthis area.
Flavio H. FentonCornell [email protected]
Elizabeth M. CherrySchool of Mathematical SciencesRochester Institute of [email protected]
Rupinder Singh, Niels F. OtaniDepartment of Biomedical SciencesCornell [email protected], [email protected]
MS121
Modeling Cardiac Electromechanics Using the Im-mersed Boundary Method
The immersed boundary (IB) method treats problems offluid-structure interaction in which an elastic structure isimmersed in a viscous incompressible fluid, using a La-grangian description of the stucture and an Eulerian de-scription of the fluid. The IB method was developed tomodel cardiac fluid dynamics, but we have extended theIB method also to model cardiac electrophysiology, therebyproviding a unified approach to simulating cardiac elec-tromechanics. This talk will describe both variants of theIB method and will present progress towards the develop-ment of IB models of cardiac electromechanics.
Boyce E. GriffithLeon H. Charney Division of CardiologyNew York University School of [email protected]
MS121
Visualizing Patterns of Cardiac Action PotentialPropagation Using Ultrasound Images of Contrac-
212 DS11 Abstracts
tion
We find that the spatial structure of mechanical deforma-tions in the heart, as obtained from ultrasound images, maybe used to reconstruct dynamical patterns of action poten-tial propagation, even though, in general, applied stressescannot be uniquely determined from the strain field theyinduce. The theory is extended to consider the role of theincompressibility assumption on this calculation and thepossibility that myocardial fiber orientation may also bedetermined from the deformation data.
Niels F. OtaniDept. of Biomedical SciencesCornell [email protected]
Rupinder SinghDept. of Biomedical EngineeringCornell [email protected]
MS122
Identifying and Characterizing Change Points Us-ing the Informational Approach
Understanding past climate abrupt shifts is a crucial steptowards learning how to predict them. Change point de-tection can be useful to detect abrupt shifts in the climatesystem. We present a general change point detection andmodel selection approach allowing to identify the timing ofabrupt shifts and to discriminate between abrupt or grad-ual changes. The usefulness of this approach to detectmajor changes that occurred in the carbon cycle is demon-strated through applications.
Claudie BeaulieuPrinceton UniversityPrinceton, [email protected]
MS122
Atmospheric Regimes, Predictability and ClimateChange
An important topic in climate science are metastableregimes in the atmosphere. Such regimes have an impor-tant influence on predictability of surface weather and thefrequency of occurrence of extremes. In my presentation Iwill introduce sophisticated methods for systematic regimeidentification. I will also discuss how regimes are relatedto low dimensional dynamical systems, their predictabilityproperties and how recent climate change has influencedtheir frequency of occurrence.
Christian FranzkeBritish Antarctic [email protected]
MS122
Recurrent Episodes of Synchrony in a Spatial Neu-ral Network Model
Epileptic seizures are regarded as short recurrent episodesof overly synchronous firing of neurons. The nature of tran-sitions into and out of seizures is not fully understood. Wepresent a spatial network model of pulse-coupled oscilla-tors which generates recurrent, self-terminated events ofsynchronous firing at random looking times even without
noise or changing control parameters. We investigate dy-namics and emergence of these events and discuss possibleimplications for seizure prediction research.
Alexander RothkegelUniversity of BonnBonn, [email protected]
Klaus LehnertzUniversity of Bonn, [email protected]
MS122
Dynamic Bifurcations with Loss of Local Stabilityin the Presence of Noise
We discuss distributions of escape times for systems under-going parameter sweeps near bifurcations in the presenceof noise, focusing on delayed bifurcations. Noise causes aloss of information about initial conditions and a spread-ing of escape times. We show that, under a linear-in-timeparameter sweep, the escape distributions are governed bya single parameter: the noise strength to sweep rate ra-tio. The results are shown to be important for bifurcationdetection in micro/nano-scale resonators.
Steve Shaw, Nicholas MillerMichigan State UniversityEast Lansing, [email protected], [email protected]
Mark I. DykmanDepartment of Physics and AstronomyMichigan State [email protected]
Chris BurgnerUniversity of California, Santa BarbaraSanta Barbara, [email protected]
Kimberly TurnerDept Mech Env EngUC Santa [email protected]
MS123
Multi-level Modeling of the Respiratory System
The respiratory system of mammals exhibits a wide rangeof phenomena, many of which are still not fully understood.Not surprisingly, different aspects of the system have beenmodeled over the years at different degrees of complexity.The ongoing modeling work of the respiratory system willserve as a motivation and provide an introduction for thisminisymposium. Some of the ideas will be illustrated onmodels of the lungs and models of the respiratory neuralnetwork.
Alona Ben-TalMassey UniversityInstitute of Information & Mathematical [email protected]
MS123
Opening and Closing the Loop in Small Networks:Simulation and Analysis of Multi-Level ‘Hybrid’
DS11 Abstracts 213
Dynamics
Experimental neuroscientists use ‘hybrid’ circuits of sim-ulated models connected to real neurons to test modelinghypotheses. A primary application is to ‘close the loop’and test that a model is capable of the dynamics expectedof it when coupled with a physical counterpart in a real-istic context. This approach is equally applicable to thefine-grained understanding of complex dynamical models,e.g. biophysical neural models of small networks. Thispresentation describes a simulation technology for buildingoptimally parsimonious descriptions with low-dimensionaldynamic components (ODEs and maps) coupled to form‘hybrid dynamical systems.’ With these tools, dynamics ofdifferent parts of the network (partitioned in state space,physical space, and time) are represented at different lev-els of abstraction, according to theories about their func-tion. These components can be mixed together so thathypotheses about lower-dimensional models can be testedcomputationally in the context of ‘trusted’ detailed mod-els. The approach is demonstrated for uncovering detailedmechanistic insight about the role of the hyperpolarization-activated Ih current in the phase-response characteristicsof a detailed central pattern generator model. The half-center oscillator model exhibits bursting activity throughmultiple ionic currents. This analysis technology is advo-cated as a new way to look at reduced modeling in neu-roscience, beyond a priori reductions such as mean field,phase averaging, or integrate-and-fire approximations.
Robert ClewleyDepartment of Mathematics and StatisticsGeorgia State [email protected]
MS123
Structure Preserving Reduction of Quasi-ActiveNeurons
We construct, confirm and analyze dimension reductiontechniques that replace the distributed RLC circuit of abranched quasi-active neuron with a significantly smallerRLC circuit that nonetheless retains the input-output be-havior of the full circuit.
Steven CoxRice [email protected]
MS123
An Equation-Free Analysis of Evolution in Collec-tive Migration
Collective motion of organisms is widespread in nature,from cell aggregations to herds of wildebeests. Individual-based models can provide novel insights to study suchquestions, but it is difficult to obtain tractable analyti-cal models that capture the essential biological dynamics.We develop an equation-free framework to analyze evolu-tionary dynamics of collective migratory strategies in anindividual-based spatially-explicit model.
Yannis KevrekidisDept. of Chemical EngineeringPrinceton [email protected]
Yu ZouDepartment of Chemical Engineering and PACM
Princeton [email protected]
Iain CouzinPrinceton [email protected]
Vishwesha GuttalPrinceton UniversityPrinceton, [email protected]
MS124
Clustering of Particles in a Deterministic Intermit-tent Flow
The clustering of particles in turbulent flows is widely dis-cussed in the context of many industrial and scientific ques-tions. In particular turbulent flows are interesting. Recentresults exist for the analysis of a fully turbulent flow takenfrom numerical simulation, and as well for stochastic flowmodels. Here, we present results for an intermittent, de-terministic model, trying to bridge between stochastic andturbulent deterministic flows.
Markus AbelUniversity of [email protected]
MS124
Caustics and Collisions in Turbulent Aerosols
We discuss the statistics of relative velocities of collid-ing particles in turbulent flows. Using a simple one-dimensional model as an example We demonstrate that thedistribution of collision velocities are substantially affectedby singularities in the particle flow, so-called caustics. Wecompute moments of collision velocities and compare themto results of numerical simulations of inertial particles sus-pended in random mixing flows. The model describes theresults of both one- and two-dimensional simulations well.Our conclusions are consistent with the hypothesis put for-ward in [Wilkinson, Mehlig, and Bezuglyy, Phys. Rev.Lett. 97 (2006) 058501], namely that the average collisionvelocity is a sum of two terms, a smooth and a singularcontribution (due to caustics).
Bernhard MehligGothenburg UnivGothenburg, [email protected]
Kristian GustavssonGothenburg Univ Gothenburg, [email protected]
MS124
PDF Approach for Particles in Turbulent Bound-ary Layers
The Full Lagrangian Method is used in a DNS of incom-pressible homogeneous isotropic turbulent flow to measurethe statistical properties of the segregation of small iner-tial particles advected with Stokes drag. We extend theprevious analyses by examining the distribution in timeof the log of the compression of an elemental volume ofparticles and show that it becomes highly non Gaussianfor moments of order higher than four. The occurrence
214 DS11 Abstracts
of singularities reaches a maximum at a Stokes number∼ 1, following a Poisson process. We also measure the ran-dom uncorrelated motion and mesoscopic components ofthe compression and show that their ratio follows the samedependence on Stokes number as that for the particle tur-bulent kinetic energy, noting also that the non Gaussianhighly intermittent part of the distribution of the compres-sion is associated with the RUM component.
Mike ReeksUniversity of [email protected]
MS124
Pattern Formation in Colloidal Explosions: Theoryand Experiments
We study the nonequilibrium patterns that emerge whenmagnetically repelling colloids, trapped by optical tweez-ers, are abruptly released, forming colloidal explosions[arxiv:1009.1930]. For multiple colloids in a single trap,we observe a pattern of expanding concentric rings. Forcolloids individually trapped in a line, we observe explo-sions with a zigzag pattern that persists even when repul-sions are weak to break the equilibrium linear symmetry.Theory and simulations quantitatively describe these phe-nomena.
Artur StraubeHumboldt University of [email protected]
MS125
On the Role of Delay for the Symmetry in the Dy-namics of Networks
The symmetry in a network of oscillators determines thespatio-temporal patterns of activity that can emerge. Westudy analytically how coupling delays affect the symmetryin the patterns of networks. We demonstrate that a cou-pling delay has some universal effects, as the advancementof the bifurcating point due to the coupling delay. Fur-ther effects, like the symmetrizing role of delays, dependon coupling topology or on the dynamics of the nodes.
Otti D’Huys
Department of Physics (DNTK)Vrije Universiteit Brussel, [email protected]
MS125
Stability and Resonance in Networks of Delay-Coupled Delay Oscillators
We extend the approach of generalized modeling to inves-tigate the stability of large networks of delay-coupled delayoscillators. When the local dynamical stability of the net-work is plotted as a function of the two delays a patternof tongues is revealed. Exploiting a link between structureand dynamics, we show for ensembles of large networksthat this pattern can be well approximated analytically.
Johannes M. HoefenerMax-Planck-Institut fuer Physik komplexer Systeme,[email protected]
MS125
Chaos Synchronization of Networks with Time-delayed Couplings
Networks of chaotic units with time-delayed couplings cansynchronize to a common chaotic trajectory. Although thetransmission time of the coupling may be very long, syn-chronization occurs without time shift. Global prop- ertiesof the network, particularly its loop structure, determineunder which conditions complete or cluster synchronizationcan be achieved. The dynam- ics of a single unit and theeigenvalue gap of the coupling matrix determine the phasediagram of zero lag chaos synchronization.
Wolfgang KinzelUniversity of Wuerzburg, [email protected]
MS125
Synchronizing Coupled Optical Oscillators withTime Delay
We examine the dynamics of networks of coupled nonlin-ear optical oscillators with time delays, to see if synchro-nization can be established. The dependence and mainte-nance of synchrony on relevant oscillator parameters andnetwork connectivity is studied. We report the results ofexperiments and numerical simulations and discuss openquestions and applications of such techniques to sensor net-works and coherent laser arrays.
Rajarshi RoyUniversity of Maryland, College Park, MD, [email protected]
MS126
Effects of Variability on Hybrid Circuits of TwoPulse Coupled Neurons
We used PRCs to construct maps probing the robustnessof phase locking with respect to temporal variability in theperiod and other forms of noise, and to heterogeneity be-tween neurons with respect to intrinsic period as well as toother parameters that influence the shape and magnitudeof the PRC. Several different types of hybrid networks oftwo single spiking or bursting neurons constructed usingthe Dynamic Clamp have been analyzed to date.
Carmen CanavierHealth Sciences CenterLouisiana State [email protected]
MS126
Cellular Mechanisms Underlying Spike-Time Reli-ability
Analyzing data from simulations and experiments, we showthat the variance of the relative phase, which can be calcu-lated from the phase-response curves of neurons and neu-ronal pairs, is a good indicator of spike-time reliability andstochastic synchronization in real and simulated neurons.This allows us to investigate the contribution of a spe-cific membrane conductance to spike-time reliability andstochastic synchronization.
Roberto F. GalanCase Western Reserve UniversityDepartment of Neurosciences
DS11 Abstracts 215
MS126
A Stochastic Dynamics Approach to Understand-ing the Mean and Variance of Phase ResponseCurves
For deterministic oscillators, there is a one-to-one map-ping between time and phase. With noise, a perturbationdelivered at a fixed time will encounter a system whosestate variable is probabilistic. Here we take a stochasticdynamics approach to understanding the evolution of thedensity function for latent phase. We examine several ap-proximations for the phase-dependent PRC variance, andalso invert this approach to estimate phase-dependent noisemagnitude from measured data.
Todd TroyerBiology DepartmentUniversity of Texas at San [email protected]
MS126
Using Dynamic Clamp as a Tool to Study NeuronalSynchronization
The dynamic clamp technique, which allows researchers tointroduce artificial voltage- or ligand-gated conductancesinto living neurons, is tailor-made for studies of synchro-nization. I will focus on recent, as-yet unpublished data,in which we have used dynamic clamp to study neuronalresponses to in vivo-like synaptic barrages and coherentactivity with high degrees of irregularity. I will also de-scribe recent work on synchronization with conduction de-lays, done in collaboration with Carmen Canavier.
John Whitedepartment of BioengineeringThe University of [email protected]
MS127
Surface Water Waves With Up an DownstreamBoundary Conditions
Standing surface waves in 2-D flow over a flat plate withup and down stream boundary conditions will be discussed.A simplified model yields analytic results compatible withexperiment. Numerical results for the full problem will bepresented, and open problems will be mentioned.
Carmen ChiconeDepartment of MathematicsUniversity of Missouri, [email protected]
MS127
Dynamics of a Front Solution for a BistableReaction-diffusion Equation with a DegenerateSpatial Heterogeneity
In this talk, we study a dynamics of a front solution witha transition layer of a bistable reaction diffusion equationwith a spatial heterogeneity in one space dimension. Inparticular, we consider the case where this spatial hetero-geneity degenerates on an interval. In this case the motionof the layer on the interval becomes so-called very slow.We will give the law of motion of the layer by constructing
an attractive local invariant manifold.
Hiroshi MatsuzawaNumazu National College of Technology [email protected]
MS127
Stability of Lax Shocks in Systems of Radiating Gas
: We study nonlinear orbital asymptotic stability of small-amplitude shock profiles of general systems of coupled hy-perboliceliptic equations of the type modeling a radiativegas. Such a model consists of systems of conservation lawscoupled with an elliptic equation for the radiation flux, in-cluding in particular the standard EulerPoisson model fora radiating gas. The method is based on the derivationof pointwise Green function bounds and description of thelinearized solution operator, with the main difficulty beingthe construction of the resolvent kernel in the case of aneigenvalue system of equations of degenerate type. This isa joint work with C. Lattanzio, C. Mascia, R. Plaza, andK. Zumbrun.
Toan NguyenDivision of Applied MathematicsBrown UniversityToan [email protected]
MS127
Dynamics near Turing patterns in Reaction-Diffusion Systems
We present results on the dynamics near stationaryspatially periodic (Turing) patterns in one-dimensionalreaction-diffusion systems. We motivate robust spectralstability assumptions and derive linear stability in Lp −Lq
spaces. The linear analysis is based on Floquet-Bloch de-compositions. We then show how techniques inspired byclassical normal form transformations can help understandnonlinear dynamics near Turing patterns.
Qiliang Wu, Scheel ArndUniversity of [email protected], [email protected]
MS128
Halos and Sprites: A Sequence of Instabilities andDynamic Attractors
The formation of a halo and the subsequent ejection of asprite is now reproduced in simulations [Luque, Ebert, Na-ture Geoscience 2009 and Geophys. Res. Lett. 2010].We will explain the underlying sequence of instabilitiesand dynamic attractors: the formation of a sharpeningscreening-ionization wave in the halo, its destabilizationinto a sprite streamer, streamer propagation as a movingboundary problem with branching instability and the re-illumination of the current-carrying sprite channel.
Ute EbertCWI [email protected]
MS128
Quantitative Simulations of Sprite Streamer Dis-
216 DS11 Abstracts
charges
Recent observational, theoretical and modeling work hasestablished that filamentary streamer discharges are thekey components of sprite phenomena. Streamer dischargesare a type of ionization waves, which are largely driven byhighly nonlinear processes in their wave fronts. In this talk,we discuss the current theory of sprite streamers and reportrecent streamer modeling results. We further show thatour streamer model successfully explains many observedproperties of sprite streamers.
Ningyu LiuPhysics and Space Sciences DepartmentFlorida Institute of [email protected]
MS128
An Introduction to Sprites: Observations and Ba-sic Phenomenology
This talk will provide a broad overview of various typesof transient electrical discharges such as sprites, elves, andjets triggered in the upper atmosphere by underlying thun-derstorm lightning. Examples of their sometimes spectacu-lar manifestations will be presented. Their salient physicalcharacteristics will be summarized, and their photochem-ical and plasma properties compared with other familiardischarge processes in the laboratory and in nature.
Davis SentmanUniversity of [email protected]
MS128
Stability of Simple Translating States in LaplacianFlows with Regularization
We present recent results on the linear and nonlinear sta-bility of translating bubbles in Laplacian growth problemsin streamer dynamics and viscous fingering, with differentforms of regularization. We give rigorous lower boundson the size of the basin of attraction for surface tensionregularization. This is consistent with a shrinking basisof attraction with small surface tension. Asymptotic andnumerical results suggest similar features for kinetic regu-larization, though there is also a collapsing scale near theback of the bubble.
Saleh A. TanveerOhio State UniversityDepartment of [email protected]
MS129
Dynamics in Finite Time - Concepts and Applica-tions
This talk will first provide an overview of finite-time dy-namics, and of hyperbolicity in both the classical and thefinite-time setting, and then present several pertinent re-sults. Specifically, the existence, non-uniqueness and ro-bustness of finite-time (un)stable manifolds will be dis-cussed, as well as the problem of detecting hyperbolicityfrom data encoded in a dynamic partition of the extendedphase space. Some of the fundamental challenges inherentto finite-time dynamics will become apparent.
Arno Berger
Mathematical & Statistical SciencesUniversity of [email protected]
MS129
General Theory for Monotone and Concave Skew-product Semiflows
We analyze the dynamics of monotone and concave skew-product semiflows, paying attention to the long-term be-havior of those semiorbits starting above a semicontinuoussubequilibrium and to the minimal sets. Several possibili-ties arise depending on the existence or absence of minimalsets strongly above the subequilibrium and the coexistenceor not of bounded and unbounded semiorbits. The resultsextend and unify previously known properties, showing sce-narios which are impossible in the autonomous or periodiccases.
Carmen Nnez, Rafael Obaya, Ana SanzUniversidad de [email protected], [email protected],[email protected]
MS129
Equivalence, Spectra and Nonautonomous Bifurca-tions
The lack of equilibria or periodic solutions for generalnonautonomous evolutionary equations requires new ideasto establish a corresponding bifurcation theory. In thissetting, the Sacker-Sell spectrum is an appropriate tool toguarantee that entire solutions persist under a large class ofperturbations. However, when it comes to bifurcations, amore detailed insight into the fine structure of the spectrumis required. On this basis, we investigate nonautonomousbifurcation scenarios and classify them using appropriatesubsets of the Sacker-Sell spectrum. In particular, theyinclude the surjectivity and Fredholm spectra.
Christian PoetzscheMunich University of [email protected]
MS129
An Alternative Approach to Sacker-Sell SpectralTheory
In the classical Sacker-Sell spectral theory, growth ratesof linear nonautonomous dynamical systems are character-ized by means of exponential dichotomies. The Sacker-Sellspectrum is given by the union of finitely many closed in-tervals, each of which is associated to a spectral manifold.This yields a linear decomposition of the extended phasespace. In this talk, we propose an alternative way to ob-tain the Sacker-Sell spectrum: In contrast to the classicalapproach, we start with a linear decomposition, which isgiven by the finest Morse decomposition in the projectivespace. Then the growth rates attained in the componentsof this Morse decomposition yield the Sacker-Sell spectrum.
Martin RasmussenImperial College [email protected]
Fritz ColoniusUniversity of Augsburg
DS11 Abstracts 217
Peter KloedenJohann Wolfgang Goethe UniversityFrankfurt am Main, [email protected]
MS130
Modeling the Dynamics of Social Competition
When groups compete for members, the resulting dynam-ics of human social activity may be understandable withsimple mathematical models. I will present a new treat-ment of this problem with several applications, but with aspecial focus on the competition for adherents between re-ligious and irreligious segments of modern secular societies.I’ll apply perturbative techniques to analyze a theoreticalframework for group competition dynamics on a network,and show that data suggest a particular case of the gen-eral framework, leading to clear predictions about possiblefuture trends in society.
Daniel Abrams, Haley YapleNorthwestern [email protected],[email protected]
Richard WienerResearch Corporation for Science AdvancementUniversity of [email protected]
MS130
Propagation of Epidemics onDynamically-adapting Networks
During an epidemic, susceptible individuals attempt toavoid contact with infectees in order to reduce their suscep-tibility. I will introduce a simple network-based of model ofthis behavior, called 2FleeSIR. As a result of changes in thecontact network, one finds categorical changes in the epi-demic’s propagation and arrives at surprising public policyquestions.
Alexander GutfraindTheoretical DivisionLos Alamos National [email protected]
MS130
Network Analysis and Dynamical Modeling of Can-cer Cells
Certain types of cancer can be ascribed to the over-expression of a single gene inducing the transition from nor-mal to the cancerous phenotype. In some type of multiplemyeloma cancer this is the case for the gene WHSC1. Over-expression of WHSC1 affects overall gene expression alongvarious gene regulatory pathways. We present a methodhow to detect and visualize these networks based on geneexpression data and propose a framework for modeling theswitching of cell phenotypes.
Michael SchnabelMax-Planck Institute for Dynamics and Self-OrganizationGottingen, [email protected]
Nir YungsterNorthwestern [email protected]
Dirk BrockmannDept. of ESAM, Northwestern UniversityEvanston, IL, [email protected]
Adilson E. MotterNorthwestern [email protected]
William KathNorthwestern UniversityEngineering Sciences and Applied [email protected]
MS130
Effect of Human Motion on Dynamic Contact Net-works
We develop a human motility model that accounts for thedisparate timescales of relocation (change of home) andtravel (with return to home) and study the effect uponthe dynamic contact network associated with the movingneighborhood around individual agents. We also considerthe effect on behaviors that reflect dynamics on that con-tact network, with implications upon (for instance) spatialspread of disease or coordinated action of a distributed setof actors.
Joseph Skufca, Daniel Ben-AvrahamClarkson [email protected], [email protected]
MS131
Modeling Signaling Pathways in Macrophages
Cell signaling pathways play a crucial role in proper celldevelopment and behavior, with implications to survival,chemotaxis, proliferation, and even programmed cell deathknown as apoptosis. In this talk, a mathematical model ofthe G-protein signaling pathway in a particular cell line ofmacrophages is outlined, focusing on activation of a par-ticular G-protein-coupled receptor, P2Y6. The model isbased on the kinetics of P2Y6 surface receptors, inositoltrisphosphate, cytosolic calcium, and differential dynam-ics of multiple species of diacylglycerol. Insight into thedynamics of the system is given through available exper-imental results and incorporated into the model. Mathe-matical analysis of the model, including establishment ofglobal existence, uniqueness, positivity, and boundednessof solutions, and global stability of a unique steady-statesolution is discussed.
Hannah CallendarInstitute for Mathematics and Its ApplicationsUniversity of [email protected]
Mary Ann HornVanderbilt University & National Science [email protected]
MS131
Models of the Innate Immune Response in Inflam-
218 DS11 Abstracts
matory Diseases
The innate immune system is vital to many species as ei-ther the predominate immune response or as a first lineof defense complementing the adaptive immune response.We will examine nonlinear models of differential and par-tial differential equations examining interactions of variousinnate defenses including: macrophage recruitment and ac-tivation through cytokine signaling, antimicrobial peptidessecretion, and the movement of the mucociliary tract lead-ing to inflammation in the respiratory system.
Meagan C. HeraldMathematics & Computer ScienceVirginia Military [email protected]
MS131
Tnf and Il-10 Are Major Factors in Modulationof the Phagocytic Cell Environment in Lung andLymph Node in Tuberculosis: a Next GenerationTwo Compartmental Model
We build a two-compartmental ODE model of the im-mune response to provide a gateway to more spatial andmechanistic investigations of Mycobacterium tuberculosisinfection in the LN and lung. Crucial immune factorsemerge that affect macrophage populations and inflamma-tion, such as TNF as a major mediator of recruitment ofphagocytes to the lungs, and IL-10, in balancing the domi-nant macrophage phenotype in LN and lung. Surprisingly,bacterial load plays a less important role than TNF in in-flammation.
Simeone MarinoUniversity of Michigan Medical SchoolMicrobiology and [email protected]
Denise E. KirschnerUniv of Michigan Med SchoolDept of Micro/[email protected]
Amy Myers, JoAnne FlynnUniversity of Pittsburgh School of MedicineDepartment of Microbiology and Molecular [email protected], [email protected]
MS131
Inflammation, Immunity, and Age: Insights fromAn In-Host Model of Influenza
Influenza A Virus triggers a complex in-host immune re-sponse including inflammatory, innate, and adaptive com-ponents. These responses change with age. We devel-oped an autonomous, nonlinear ODE model of the host-virus dynamic dynamic in 20 dimensions and 90 parame-ters. Parameter estimation was employed to fit the modelagainst data sets from two cohorts of BALB/c mice, oneaged 2-4 months and the other 18-24, yielding marginalPDFs of parameters values. These are compared betweencohorts, yielding well-defined hypotheses as to the mecha-nistic changes of the host-virus response with age.
Ian PriceUniversity of [email protected]
MS132
The Alternans Annihilation byDistributed Mechano-electric and Boundary Pac-ing Applied Perturbations
Alternans is a life-threatening physiological condition ofthe cardiac tissue in which there is alteration in electrome-chanical response between beats of a periodically simulatedcardiac tissue. In this work we demonstrate the annihila-tion of cardiac alternans using mechanical perturbation.We explore from a control point of view a computationalframework that employs electromechanical and mechano-electric feedback to couple a two variable Aliev - Panfilov(1996) model with the non-linear stress equilibrium equa-tions.
stevan DubljevicUniversity of [email protected]
MS132
Model-based Control of Alternans in PurkinjeFibers
We describe a systematic approach to suppressing cardiacalternans in Purkinje fibers using localized current injec-tions. We investigate the controllability and observabilityof the periodically paced Noble model for different loca-tions of the recording and control electrodes along the fiberand determine how the optimal locations for the electrodesand the timing of the feedback current can be selected toextend the length of the fiber over which alternans can besuppressed.
Roman GrigorievGeorgia Institute of TechnologyCenter for Nonlinear Science & School of [email protected]
Alejandro GarzonGeorgia Institute of [email protected]
MS132
Control of Cardiac Cellular Alternans Induces Sub-cellular Turing Pattern in Calcium Dynamics
Cardiac alternans is a dangerous rhythm disturbance of theheart, in which rapid stimulation elicits a beat-to-beat al-ternation in the action potential duration and calcium tran-sient amplitude of individual myocytes. Recently, ‘subcel-lular alternans,’ in which the calcium transients of adjacentregions within individual myocytes alternate out-of-phase,has been observed. Using experiments and computationalmodeling, we show that subcellular alternans is a strikingexample of a biological Turing instability.
Stephen Gaeta, Trine Krogh-MadsenCornell University - Weill Medical [email protected], [email protected]
David ChristiniCornell University - Weill Medical CollegeDivision of [email protected]
MS132
Reconstruction of Unmeasured Quantities in Mod-
DS11 Abstracts 219
els of Cardiac Action Potential Dynamics
In this study, closed-loop observer techniques were in-vestigated as a means of reconstructing unmeasured car-diac variables. Such methods may lead to improved anti-arrhythmic stimulus protocols. Luenberger feedback wasshown to stabilize a multi-cell observer based on the two-variable Karma model of action potential (AP) dynamics.An observer applied to microelectrode data from an in vitrocanine Purkinje fiber was able to estimate AP durationsaway from sensor locations. Extensions to ion-channelmodels will be discussed.
Laura MunozDepartment of Biomedical SciencesCornell [email protected]
Niels F. OtaniDept. of Biomedical SciencesCornell [email protected]
MS133
Multi-Layered Networks and Emergency of Spatio-temporal Order in Ecological Systems
Evolutionary-game based models, in which the success ofone species depends on the behaviour of the others, havebecome paradigmatic to explain species coexistence in eco-logical systems. The generic properties of the competitioncan be characterized by the rock-paper-scissors game incombination with spatial dispersal of static populations.I will consider a complex network, defined on a lattice orpopulation patch in which the interaction among the nodeschanges the state of the nodes stochastically.
Celso GrebogiKing’s CollegeUniversity of [email protected]
MS133
Dynamics of Large-Scale Epileptic Brain Networks
Approaches from complex network theory promise to im-prove understanding of the epileptic process through theanalysis of interactions in large-scale human brain net-works. We present recent findings obtained from analy-ses of interaction networks derived from measurements ofbrain dynamics in epilepsy patients. We discuss pros andcons of previous analysis approaches and address possiblemethodological advancements that are necessary to furtherimprove assessment of the dynamics of epileptic brain net-works.
Klaus LehnertzDept. of Epileptology, Medical CenterUniversity of Bonn, [email protected]
Marie-Therese Kuhnert, Stephan BialonskiUniversity of Bonn, [email protected],[email protected]
MS133
Direction of Information Flow in Networks
The inference of causal interaction structures in multivari-ate systems enables a deeper understanding of the inves-tigated network. We discuss two shortcomings, which areoften faced in applications, i.e. nonstationarity of the pro-cesses generating the time series and contamination withobservation noise. To overcome both, we present a new ap-proach by combining partial directed coherence with statespace models. The performance is illustrated by means ofmodel systems and in an application to neurological data.
Linda SommerladeFreiburg Center for Data Analysis and ModelingUniversity of [email protected]
Jens TimmerUniversity of FreiburgDepartment of [email protected]
Bjorn SchelterFreiburg Center for Data Analysis and ModelingUniversity [email protected]
MS133
Modelling Brain States by Adaptive Multiple-Time-Scale Networks
We will present a model of the transition between differentactivity states in networks, with an application to EEGdata for different sleep-wake states. Our approach is basedon interacting ARMA processes with dynamically changingparameters. The model can not only describe normal EEGactivity but also models the transitions between wake, sleepand REM sleep phases. We study how on an longer timescale Alzheimer’s Disease impacts the transitions betweendifferent sleep states.
Marco ThielDepartment of Physics - King’s CollegeUniversity of Aberdeen, [email protected]
Bjoern SchelterCenter for Data Analysis and ModelingUniversity of Freiburg, [email protected]
MS134
Perturbation Theory for the Approximation of Sta-bility Spectra by QR Methods for Products of Lin-ear Operators
We develop a perturbation analysis for stability spectra(Lyapunov exponents and Sacker-Sell spectrum) for prod-ucts of operators on a Hilbert space based upon the discreteQR technique. Error bounds are obtained in both the inte-grally separated and non-integrally separated cases and forboth real and complex valued operators. We illustrate ourresults using a linear parabolic partial differential equationin which the strength of the integral separation determinesthe sensitivity of the stability spectra.
Mohamed Badawy, Erik Van VleckDepartment of Mathematics
220 DS11 Abstracts
University of [email protected], [email protected]
MS134
Evolution Families and Lyapunov Exponents forRetarded Dynamical Systems
The knowledge of Lyapunov and other stability spectra isfundamental in understanding complex nonlinear dynam-ics. Computational techniques have been established toaddress the problem for Ordinary Differential Equations:here we briefly recall the basic ideas behind QR methods.Then we present how their use can be extended to theinfinite dimensional case of Delay Differential Equations,by discretizing the associated evolution family. Theoreti-cal as well as implementation and convergence issues arediscussed.
Dimitri BredaDepartment of Mathematics and Computer ScienceUniversity of [email protected]
MS134
Detecting Exponential Dichotomy on the Real Line
In this talk we propose numerical techniques based on theQR factorization and on the SVD to ascertain exponentialdichotomy on the entire real line. Methods to detect ex-ponential dichotomy for special classes of systems are wellestablished in the literature, e.g. Hamiltonian systems andsystems with asymptotically constant coefficient matrices.Instead we propose and justify techniques which apply togeneral linear systems. We show the behavior of our meth-ods with several numerical examples.
Cinzia EliaUniversity of [email protected]
MS134
Stability Spectra: Approximation and Perturba-tion Theory
In this talk we provide background on the approximationof stability spectra (Lyapunov exponents and Sacker-Sellspectrum) and on specific issues to be discussed in thisminisymposium. These include the approximation of sta-ble and unstable subspaces using matrix factorizations offundamental matrix solutions, error analysis for approxi-mation of stability spectra for sequences of linear operatorsin Hilbert space, and the approximation of stability spectrafor linear time dependent retarded delay equations.
Erik Van VleckDepartment of MathematicsUniversity of [email protected]
MS135
A Model for Odor Discrimination in the HoneybeeAntennal Lobe
The honeybee antennal lobe (AL) provides an ideal sys-tem to study the olfactory system because it is anatom-ically and genetically simpler than the olfactory bulb ofmammals. While anatomical structures within the AL arerelatively well known, their functional roles remain poorly
understood. We made a mathematical model to explorethe possible network connectivities which can reproduceseveral features of experimental results such as a smoothtransition patterns for detecting different odors.
Sungwoo AhnDepartment of Mathematical SciencesIndiana University Purdue University [email protected]
David H. TermanThe Ohio State UniversityDepartment of [email protected]
MS135
Functional Aspects of Olfactory Processing: Neu-ral Rhythms, Dynamics of Input/output NeuralActivity and Overview of Related Olfactory Mod-els
Using subspace analysis methods on optical imaging datafrom the olfactory bulb, we investigate how dynamics ofodor responses in the primary receptor neurons of awakerats are shaped by the temporal features of the active odorsniffing. We use these data as input for computationalmodels of endogenously bursting external tufted cells ormitral/tufted cells to investigate the structure of the in-put/output in the olfactory neural network.
Remus OsanBoston UniversityDepartment of [email protected]
Eric SherwoodBoston [email protected]
MS135
Functional Roles for Synaptic Depression Withinthe Fly Antennal Lobe
Several experiments indicate that there exists substan-tial synaptic-depression at the synapses between olfac-tory receptor neurons (ORNs) and neurons within thedrosophila antenna lobe (AL). This synaptic-depressionmay be partly caused by vesicle-depletion, and partlycaused by presynaptic-inhibition due to the activity of in-hibitory local neurons within the AL. While it has beenproposed that this synaptic-depression contributes to thenonlinear relationship between ORN and projection neuron(PN) firing-rates, the precise functional role of synaptic-depression at the ORN–AL synapses is not yet fully under-stood. I believe that the mechanisms of vesicle-depletionand presynaptic-inhibition may be balanced within the flyAL in order to optimize the fine odor-discrimination capa-bilities of this network over short observation times (of afew hundred milliseconds). I will briefly introduce and de-scribe the subnetwork analysis I used to substantiate thishypothesis within a rather general class of neuronal net-work models.
Aaditya RanganCourant Institute of Mathematical SciencesNew York [email protected]
DS11 Abstracts 221
MS135
Network Adaptation Through Activity-dependentRestructuring: Neurogenesis Enhances OlfactoryPattern Separation
The neuronal turn-over associated with adult neurogene-sis leads to a persistent restructuring of the network ofthe olfactory bulb that depends on the activity of the neu-rons. Within the framework of a minimal network modelwe show that this allows the network to learn to decorrelateinput patterns representing similar odor stimuli. For thediscrimination of similar mixtures the model makes spe-cific predictions about the dependence of the performanceon the learning protocol.
Hermann RieckeApplied MathematicsNorthwestern [email protected]
Siu Fai ChowNorthwestern [email protected]
MS136
Instability of Twinned Orbits in a Coupled Respi-ratory Bursting Neuron Model
Let f : Rn ×Rn → Rn be a smooth vector field and let thesystem
x = f(x, x) (1)
have a stable periodic orbit x = γ(t). By symmetry, thesystem
x = f(x, y), y = f(y, x) (2)
will have a periodic orbit x = γ(t), y = γ(t). We call such asolution of (2) a pair of twinned orbits. We study the effectsof parametric heterogeneity on the stability of twinned or-bits in a model of coupled bursting neurons of the respi-ratory central pattern generator in the pre-Botzinger com-plex of the mammalian brain stem.
Casey O. DiekmanThe Ohio State [email protected]
Peter Thomas, Chris WilsonCase Western Reserve [email protected], [email protected]
MS136
Network Bursting: Interactions of the CAN andNaP Currents
The CAN and persistent sodium currents have been pro-posed to play key roles in respiratory rhythmogenesis. Pre-vious modeling demonstrated that each current can under-lie a bursting pattern with distinctive features. We presenta slow-fast decomposition analysis of a unified neuronalmodel including both currents. Interactions of these cur-rents create novel bursting patterns and synergistically pro-mote robust bursting. We also study dynamics of a het-erogeneous collection of these model neurons coupled in abiologically motivated architecture.
Justin DunmyreUniversity of [email protected]
Christopher Del NegroCollege of William and [email protected]
Jonathan E. RubinUniversity of PittsburghDepartment of [email protected]
MS136
Multiple Bursting Mechanisms in HeterogeneousNeural Populations with Metabotropic GlutamateReceptors and NaP and CAN Currents
We investigated a series of mathematical models of sin-gle neuron and neural populations with excitatory inter-connections incorporating the intrinsic mechanisms thatwere suggested to operate in the pre-Botzinger Com-plex (pre-BotC). These mechanisms include persistentsodium current-dependent bursting, IP3-dependent cal-cium oscillations, synaptically activated IP3-productionand calcium-activated cation-nonspecific current. Wedemonstrated the co-existence of several qualitatively dif-ferent oscillatory mechanisms depending on model parame-ters which may be relevant to rhythmic activities observedin the pre-BotC and spinal cord.
Yaroslav Molkov, Patrick Jasinski, Natalia Shevtsova,Ilya A. RybakDrexel University College of [email protected], [email protected],[email protected], [email protected]
MS136
Interaction of the Two Distinct Bursting Mecha-nisms in the Model of Respiratory Neuron
Motivated by experimental evidence of two types of burst-ing neurons in the pre-Btzinger complex of the medulla,we present a two-compartment mathematical model of apre-Btzinger neuron with two independent bursting mech-anisms. Bursting in the somatic compartment is modeledvia inactivation of a persistent sodium current, whereasbursting in the dendritic compartment relies on intrinsiccalcium oscillations. Interaction of the two distinct burst-ing mechanisms in the model explains complex burstingactivity observed in experiments.
Natalia Toporikova, Robert ButeraGeorgia Institute of [email protected], [email protected]
MS137
Biological Change Detection: Relating InformationAcquired to Mechanism Employed
Sensitivity to rates of change in associated stimuli havebeen reported from multiple biological sensory systems in-cluding bacterial gene networks, vertebrate immune cellsand even arthropod neuroendocrinology. There has been,however, very little effort to establish a unified analysisof change detection across these disparate scientific disci-plines. Using a dynamical systems approach, we highlightsimilarities and differences among change detection mech-anisms that have been reported and/or proposed across avariety of research fields.
Sharon A. Bewick
222 DS11 Abstracts
NIMBioS and University of Tennessee, Knoxvillesharon [email protected]
MS137
T Cell State Transitions Produce an EmergentChange Detector
We develop a model using a system of ordinary differentialequations that shows how T cells can detect changes inantigen levels. A key component of this detector is naıve Tcell activation. The activation step creates a barrier thatseparates the slow dynamics of naıve T cells from the fastdynamics of activated T cells. This separation generates anadaptive system that continually compares shifts in antigenstimulation to long-term, steady state levels.
Peter S. KimUniversity of UtahDepartment of [email protected]
Peter LeeStanford UniversitySchool of [email protected]
MS137
A Control-Oriented Model for Immune RegulatoryResponse: Pid Control with Switching
In this talk, we develop a model of the immune system as acontrol system which regulates infectious agents. In partic-ular, we take known data and models of the action of IL-2and Treg growth and show how they describe a differentialcontroller with on-off switching and an integral feedbackreset. We hypothesize that the body uses differential con-trol to differentiate self from non-self. We use numericalsimulation to justify our interpretation of the model.
Matthew M. PeetIllinois Institute of [email protected]
Peter S. KimUniversity of UtahDepartment of [email protected]
Peter LeeStanford UniversitySchool of [email protected]
MS137
Growth Detection: CD4+ T-cells Interaction Net-works as an Interface for Immune System Decision-Making based on Changes in Antigen Load
Recently, a number of experiments have suggested thatantigen kinetics play a role in immune system decision-making. The mechanisms underlying this mode of immunesystem regulation, however, are unknown. We develop asystem of ordinary differential equations to describe sig-naling between Th1, Th2, Th17 and iTreg cells and showthat this CD4+ T-cell interaction network is capable of ac-curately and robustly classifying pathogens based on pop-
ulation growth rates.
Routing YangUniversity of California, Santa [email protected]
Sharon A. BewickNIMBioS and University of Tennessee, Knoxvillesharon [email protected]
Mingjun ZhangMechanical, Aerospace and Biomedical EngineeringDepartmentUniversity of Tennessee, [email protected]
MS138
Existence of Defects in Swift-Hohenberg Equations
We show the existence of grain boundaries and disloca-tions in the classical Swift-Hohenberg equation and in ananisotropic Swift-Hohenberg equation, respectively. Wefind these defects as traveling waves connecting roll pat-terns with different wavenumbers. The analysis relies upona spatial dynamics formulation of the bifurcation problem,a local center-manifold reduction, and normal form theory.We also discuss possible extensions and limitations of ourapproach.
Mariana HaragusLaboratoire de Mathematiques de BesanconUniversite de Franche-Comte, [email protected]
Arnd ScheelUniversity of MinnesotaSchool of [email protected]
MS138
On the Mechanisms for Instability of StandingWaves in Nonlinearly Coupled Schrodinger Equa-tions
Dynamical systems methods have been used with greatsuccess to identify nonlinear waves, and also to charac-terize the stability of those waves. For instance, when ashooting method is used to pinpoint a standing wave, asecond shooting method in a related space can often beused to locate eigenvalues of the linearized operator at thestanding wave. In this talk, we use these methods to de-tect instabilities in many of the standing waves (both 1-pulses and N-pulses) found in nonlinearly coupled systemsof Schrodinger equations.
Russel JacksonUS Naval [email protected]
MS138
Stability Analysis for Closed Curve Solutions to theVortex Filament Equation
In its simplest form, the self-induced dynamics of a vortexfilament in a perfect fluid is governed by the Vortex Fila-ment Equation (VFE), a nonlinear partial differential equa-tion that is related to the Nonlinear Schroedinger (NLS)equation via the well-known Hasimoto map. The NLS is
DS11 Abstracts 223
integrable and admits a corresponding AKNS linear sys-tem. The squared eigenfunctions of the AKNS system playa central role in linear stability studies of solutions of theNLS equation, as they provide a large (and often complete)set of solutions of the linearization of the NLS equationabout a given solution. Using the squared eigenfunctionsand the relation between the VFE and NLS equations, weconstruct solutions of the linearized VFE equation and re-late the stability properties of vortex filaments to those ofthe associated NLS potentials.
Stephane LafortuneCollege of CharlestonDepartment of [email protected]
MS138
On the Traveling Waves of Gray-Scott Model
For a wide range of parameter values we show the existenceof rich families of traveling waves of the Gray-Scott model.We find pulse solutions, periodic wave trains, families offronts that connect constant states, constant states to aperiodic wave train, two periodic wave trains, a periodicorbit to a pulse train. In certain singular limits we pin-point the structure of the traveling waves. The results areanchored in geometric singular perturbation theory.
Vahagn ManukianMiami [email protected]
MS139
Multiple Injection Dynamics in Two-mode Lasers
A two-mode laser diode under simultaneous optical injec-tion in both modes shows dynamical features which areremarkably different from the well studied single mode in-jection case. In particular the double-locked equilibriumstates, where both modes are locked to the respective in-jected signal, gives rise to interesting phenomena. We iden-tify a region of bistability between double-locked states,which allow for the realisation of a fast all-optical mem-ory element. The theoretical predictions are confirmed byexperiments.
Andreas Amann, Simon Osborne, Patrycja Heinricht,Benjamin Wetzel, Stephen O’BrienTyndall National InstituteUniversity College Cork, Cork, [email protected], [email protected], [email protected], [email protected],[email protected]
MS139
From Phase Locking to Optical Turbulence in Cou-pled Lasers
We study synchronisation properties of three coupled laserswith S1 ×Z2-symmetry. Conditions for the stability of in-phase and anti-phase locking are calculated analytically asfunctions of the coupling strength and frequency detuningbetween the lasers, and the amplitude-phase coupling ofa single laser (also known as non isochronicity). Bifurca-tion analysis and Lyapunov exponents reveal interestingsymmetry breaking phenomena including transitions be-tween synchronised and unsynchronised chaos (optical tur-
bulence) due to blowout bifurcations.
Nicholas BlackbeardMathematics Research InstituteUniversity of Exeter, Exeter, [email protected]
Hartmut Erzgraber, Sebastian M. WieczorekUniversity of ExeterMathematics Research [email protected], [email protected]
MS139
Broadband Chaos Generated by an OptoelectronicOscillator
We discuss the dynamics of an optoelectronic time-delayoscillator that displays high-speed chaotic behavior witha flat, broad power spectrum. Experimentally we findthat the chaotic state coexists with a linearly-stable fixedpoint, which, when subjected to a finite-amplitude pertur-bation, loses stability initially via a periodic train of ultra-fast pulses. We derive approximate mappings that do anexcellent job of capturing the observed instability.
Lucas IllingReed [email protected]
Kristine Callan, Zheng GaoDepartment of PhysicsDuke University, Durham, North [email protected], [email protected]
Daniel GauthierDepartments of Physics and Biomedical EngineeringDuke [email protected]
Eckehard SchoellInstitute for Theoretical PhysicsTechnical University [email protected]
MS139
Optimal Topologies for Synchronization in a Net-work of Chaotic Optoelectronic Oscillators
Synchronization in a network of coupled oscillators is in-fluenced by the dynamical nature of the nodes and theinteraction topology. Here, we present an experimentalexploration of the influence of various network topologieson the synchronization of a network of chaotic optoelec-tronic oscillators. For networks with varying number ofconnections, we measure the rate of convergence to a syn-chronous solution. The rate to synchronization is observedto be maximal when there are a quantized number of linksin the network.
Bhargava RavooriUniversity of Maryland, College ParkDept. of [email protected]
Rajarshi RoyUniversity of [email protected]
224 DS11 Abstracts
MS140
Improved Linear Response for StochasticallyDriven Systems
The recently developed short-time linear response algo-rithm, which predicts the average response of a nonlinearchaotic system with forcing and dissipation to small ex-ternal perturbation, generally yields high precision of theresponse prediction, although suffers from numerical in-stability for long response times due to positive Lyapunovexponents. However, in the case of stochastically drivendynamics, one typically resorts to the classical fluctuation-dissipation formula, which has the drawback of explicitlyrequiring the probability density of the statistical state to-gether with its derivative for computation, which might notbe available with sufficient precision in the case of com-plex dynamics (usually a Gaussian approximation is used).Here we adapt the short-time linear response formula forstochastically driven dynamics, and observe that, for shortand moderate response times before numerical instabilitydevelops, it is generally superior to the classical formulawith Gaussian approximation for both the additive andmultiplicative stochastic forcing. Additionally, a suitableblending with classical formula for longer response timeseliminates numerical instability and provides an improvedresponse prediction even for long response times.
Rafail AbramovDepartment of Mathematics, Statistics and ComputerScienceUniversity of Illinois at [email protected]
MS140
Estimating Error Probabilities in Noise-PerturbedNonlinear Optical Systems
Many lightwave systems are designed to operate with strin-gent performance requirements. In such cases, the inter-play between noise and nonlinearity makes the estimationof error probabilities a challenging task: analytical meth-ods cannot deal with the complexity of these systems, andbrute-force numerical approaches are completely impracti-cal. An approach that has been shown to be very effectiveis the combination of analytical tools (such as large devi-ation theory) with variance reduction techniques (such asimportance sampling). This talk will provide an overviewof the problem and a review of recent results, includingthose for dispersion-managed systems and phase-sensitiveproblems.
Gino BiondiniState University of New York at BuffaloDepartment of [email protected]
MS140
Stochastic Integrable Dynamics in Active OpticalMedia
Resonant interaction of light with a randomly-prepared,lambda-configuration active optical medium is describedby exact solutions of a completely-integrable, random par-tial differential equation, thus combining the opposing con-cepts of integrability and disorder. An optical pulse pass-ing through such a material will switch randomly betweenleft- and right-hand circular polarizations. Exact proba-bility distributions of the electric-field envelope variablesdescribing the light polarization and their switching times
will be presented .
Gregor KovacicRensselaer Polytechnic InstDept of Mathematical [email protected]
Ethan AtkinsCourant [email protected]
Ildar R. GabitovDepartment of Mathematics, University of [email protected]
Peter R. KramerRensselaer Polytechnic InstituteDepartment of Mathematical [email protected]
MS140
Sub-sampling in Parametric Estimation of EffectiveStochastic Models from Discrete Data
In this talk we address the problem of stochastic modelingof large-scale essential variables from discrete time-series.Parameters in stochastic parametrizations are estimatedfrom the discrete time-series of the essential variables aloneand no knowledge of small-scales is necessary. In partic-ular, we analyze the dependence of the linear OU-typeparametrizations on the sampling time-step. It has beenrecognized that the stochastic terms are not appropriate tomodel smooth trajectories at small lags because the under-lying trajectory is fundamentally different from the samplepath of a stochastic system. Nevertheless, the main prac-tical goal is to determine a closed-form low-dimensionalsystem resembling the behavior of large scale structures onlonger time-scales. To achieve this goal, the dataset hasto sub-sampled (i.e. rarefied) to ensure estimators’ consis-tency. Nevertheless, we show that estimators are biasedfor any finite sub-sampling time-step and construct newbias-corrected estimators. Numerical examples of variouscomplexity will be presented to illustrate the concept.
Ilya TimofeyevDept. of MathematicsUniv. of [email protected]
MS141
Relative Equilibria of the (1+N)-vortex Problem
We study relative equilibria of the (1 + N)-vortex prob-lem where N vortices have small, equal circulation andone vortex has large circulation. In the limit, the problemreduces to seeking critical points of a particular potentialfunction defined on a circle. In contrast to the Newtonian(1+N)-body problem, there are typically multiple relativeequilibria for both small and large N. Linear stability isalso studied, and situations are found where there are nostable relative equilibria.
Anna BarryMathematicsBoston [email protected]
Glen R. HallBoston University
DS11 Abstracts 225
C. Eugene WayneBoston UniversityDepartment of [email protected]
MS141
Point Vortex Equilibria and Optimal Packings ofCircles on a Sphere
We answer the question of whether optimal packings ofcircles on the sphere are equilibrium solutions to the log-arithmic particle interaction problem on the sphere (i.e.point vortices) for N = 3-12 and 24, the only values of Nfor which optimal packings are rigorously known. We alsowill describe algorithms associated with the formation andassembly of these and other equilibrium configurations onthe sphere which involve clustering sub-groups of particlesduring random walk formation. P.K. Newton, T. Sakajo‘Point vortex equilibria and optimal packings of circles onthe sphere’, in press, Proc. Roy. Soc. A.
Paul NewtonUniv Southern CaliforniaDept of Aerospace and Mechanical [email protected]
MS141
High Order Three Dimensional Lagrangian Meth-ods Based on Deforming Ellipsoids
Vortex methods are numerical schemes for approximatingsolutions to the Navier-Stokes equations using a linear com-bination of moving basis functions to approximate the vor-ticity field of a fluid. Typically, the basis function velocityis determined through a Biot-Savart integral applied at thebasis function centroid. Since vortex methods are naturallyadaptive, they are advantageous in flows dominated by lo-calized regions of vorticity such as jets, wakes and bound-ary layers. While they have been successful in numerousengineering application, the complexity of understandinggrid-free methods make their analysis a uniquely mathe-matical endeavor. One outcome of rigorous analysis is annew naturally adaptive high order 2D method with ellip-tical Gaussian basis functions that deform as they moveaccording to flow properties. This new class of methods isvery unusual because the basis functions do not move withthe physical flow velocity at the basis function centroid as isusually specified in vortex methods. We now extend theseresults to three dimensions. The resulting analysis leads todeforming, ellipsoidal basis functions capable of achievinghigh spatial order. We will discuss the latest results onour efforts to develop a complete 3D vortex method withadaptive, deforming blobs.
Louis F. Rossi, Claudio TorresUniversity of [email protected], [email protected]
MS141
Multi-moment Vortex Methods for 2D Viscous Flu-ids
In this talk we introduce a new vortex method which incor-porates Hermite moment corrections to radially symmet-ric Gaussian basis functions. Convergence of the Hermiteexpansion is proven and the added Hermite moments al-
low for each particle to deform under convection. We willimplement this multi-moment vortex method for a tripolerelaxation example and demonstrate the improvement inspatial accuracy achieved by allowing the basis functionsto deform. Time permitting, we will discuss the trade off inthis method between computational efficiency and spatialaccuracy.
David T. UminskyDept. of [email protected]
C. Eugene WayneBoston UniversityDepartment of [email protected]
Alethea BarbaroUCLADepartment of [email protected]
Vitalii OstrovskyiUSCDepartment of [email protected]
MS142
Dynamic Centality in Real World Networks
Novel, dynamic network centrality measures will be intro-duced: NetworGame program interprets game centralityas the ability of a networked agent with a single alternat-ing strategy to change an overall starting cooperation todefection and vice versa. The Turbine program shows theextremes of low- and high-perturbing network positions.The ModuLand modularization method-family [Kovacs etal., PLoS ONE 7:e12528] helps to find role of nodes in com-munity overlaps in information processing, spatial games,perturbations, etc.
Peter CsermelySemmelweis University, Department of Medical [email protected]
Miklos AntalSemmelweis University, Dept. Med. Chem. LINK-GroupBudapest Univ. Techn. Econ, Dept. Envir. [email protected]
Huba KissSemmelweis University, Dept. Med. Chem. LINK-GroupSemmelweis University, Dept. [email protected]
Istvan KovacsSemmelweis University, Dept. Med. Chem. LINK-GroupEotvos Univ, Dept. Physics & Res. Inst. Solid [email protected]
Agoston MihalikSemmelweis University, Dept. Med. Chem. [email protected]
Gabor Simko
226 DS11 Abstracts
Semmelweis University, Dept. Med. Chem. LINK-GroupVanderbilt [email protected]
Kristof SzalaySemmelweis University, Dept. Med. Chem. [email protected]
MS142
Network Synchronization in a Noisy Environmentwith Time Delays
Time delays in transmitting and processing information arepresent in most real communication and information net-works, including info-social and neurobiological networks.Here, we discuss the impact of time delays in stochas-tic synchronization (or coordination) problems in complexnetworks. We establish the scaling theory for the phaseboundary and for the fluctuations in the synchronizableregime. Our results also imply the potential for optimiza-tion and trade-offs in synchronization and coordinationproblems with time delays [D. Hunt, G. Korniss, and B.K.Szymanski, Phys. Rev. Lett. 105, 068701 (2010)].
Gyorgy KornissPhysics. [email protected]
David HuntDepartment of Physics, [email protected]
Boleslaw SzymanskiComputer Science DepartmentRensselaer Polytechnic [email protected]
MS142
Center Manifolds, Bifurcations and Noise inStochastic Network Dynamics
Using a prototypical network model based on signaling be-tween nodes, we show the generic role of noise in switchingfrom total synchrony to asynchronous modes in networks,by embedding the nonequilibrium stochastic dynamics ofthe NamingGame in a class of singularly-perturbed ergodicnetwork models. The stochastic-dynamics of the NG yieldssolvable random walk models that support center manifoldbifurcations such as a codim-1 saddle-node and global at-tractors in the form of spatial-synchrony.
Chjan C. LimMathematical Sciences, [email protected]
Weituo ZhangRPI Network Science Center andMath [email protected]
MS142
Isolated and Composite Networks
We introduce the “modern theory of networks’, and de-scribe specific examples including the very recent paper[S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, andS. Havlin,“Catastrophic Cascade of Failures in Interdepen-dent Networks’ Nature 464, 1025 (2010)] showing that sys-
tems comprised of more than one network are vastly moresusceptible to failure cascades than isolated networks.
H. Eugene StanleyCenter for Polymer Studies and Department of PhysicsBoston [email protected]
MS143
Painting Chaos: Computational Methods for Ex-ploration of Complex Behaviors
Using the state-of-the-art numerical ODE solver TIDES,we show how combined symbolic and numerical methodscan yield a detailed information on systems in questions,that is hardly available in other settings. We will presentthe toolkit including Lyapunov exponents, fast-chaos in-dicators, template analysis of attractors, ’shrimp’ analysisfor detecting cod-2 T-points that organize globally and uni-versally the parameter space of several canonical models.We will demonstrate the tools in application to neuronalmodels as well.
Roberto BarrioUniversity of Zaragoza, [email protected]
Andrey ShilnikovNeuroscience Institute and Department of MathematicsGeorgia State [email protected]
MS143
Parameter Space Classification of Stable Solutionsof Flows
Bifurcation analysis based on numerical continuation tech-niques are frequently used to generate phase diagrams mix-ing on a single diagram curves corresponding to both stableand unstable orbits. Chaotic phases are rarely delimitedand without ever scrutinizing their inner structure. How-ever, realistic applications demand, first, classifying sta-ble behaviors, second, competent description of the innerstructure of chaotic phases, third, description of unstablephenomena that impact the previous two. We discuss twoalgorithms to face such challenges.
Jason GallasInstituto de Fisica da UFRGSPorto Alegre [email protected]
MS143
Complex Spontaneous Oscillations and ResponseProperties of Sensory Hair Cells
We use a Hodgkin-Huxley type model of a saccular hair cellto study how its mechanical and electrical compartmentsinteract to produce coherent self-sustained oscillations andhow this interaction contributes to the overall sensitivityand selectivity to external stimuli. In a wide range of pa-rameters the dynamics of the cell may become chaotic, re-sulting in broad-band encoding of external vibrations. Onthe other hand, bi-directional compartments coupling mayresult in significant enhancement of oscillation coherence,frequency selectivity and sensitivity of the cell to externalstimuli.
Alexander Neiman
DS11 Abstracts 227
Department of Physics and AstronomyOhio [email protected]
Andrey ShilnikovNeuroscience Institute and Department of MathematicsGeorgia State [email protected]
MS143
The Hindmarsh-Rose Neuron Model: Understand-ing the Bifurcation Scenario by Combining Contin-uation and Brute-force Computational Methods
The Hindmarsh-Rose neuron model is analyzed in a two-dimensional parameter space by combining theoreticaltools with numerical brute-force and continuation tech-niques. The brute-force techniques, based on numericalODE solvers, are used to classify stable periodic solutionsaccording to the number of spikes per period and to indexthe complexity of chaotic solutions. Continuation tech-niques, based on AUTO, and theoretical tools are used tounfold the complete bifurcation scenario, organized by fewcodimension-two bifurcation points.
Marco StoraceBiophysical and Electronic Engineering Department,University of Genoa, [email protected]
Daniele LinaroBiophysical and Electronic Engineering DepartmentUniversity of [email protected]
PP1
Desynchronization Bifurcation of Coupled Nonlin-ear Dynamical Systems
We analyze the desynchronization bifurcation in the cou-pled Rossler oscillators. After the bifurcation the coupledoscillators move away from each other with a square rootdependence on the parameter. We define system transverseLyapunov exponents and in the desynchronized state oneis positive while the other is negative implying that oneoscillator is trying to fly away while the other is holding it.We give a simple model of coupled integrable systems thatshows a similar phenomena and can be treated as the nor-mal form for the desynchronization bifurcation. We con-clude that the desynchronization is a pitchfork bifurcationof the transverse manifold.
Suman AcharyyaPhysical Research Laboratory, Ahmedabad, [email protected]
R. E. AmritkarPhysical Research Laboratory,Ahmedabad, [email protected]
PP1
Learning from the Past: Empirical Correction ofModels of Natural Chaotic Phenomena
The chaotic nature of Earth’s atmosphere drives weatherforecasts away from reality exponentially. Even assumingperfect atmospheric state estimates, discrepancies between
nature and models produce this divergence. In this presen-tation we demonstrate a principled approach to the miti-gation of those discrepancies. Empirical correction is ap-plied to: 1) align Lorenz systems with different parameter-values; and 2) couple 3-dimensional Lorenz-like models toa natural convection loop. Finally, we consider the tech-nique’s application to weather and climate models.
Nicholas A. AllgaierThe University of [email protected]
Kameron D. HarrisUniversity of [email protected]
Chris DanforthMathematics and StatisticsUniversity of [email protected]
PP1
Numerical Study of Existence, Stability and Colli-sion Properties of Dark-Bright Discrete Solitons
We numerically explore the existence and stability prop-erties of different configurations of dark- bright solitons,dark-bright soliton pairs and pairs of dark-bright and darksolitons in discrete settings. We consider collisions be-tween dark-bright solitons and between dark-bright anddark ones. In the regime where the underlying lattice struc-ture matters, we find a wide range of potential dynamicaloutcomes depending on the initial soliton velocity.
Azucena AlvarezUniversidad de Sevilla. Departamento de [email protected]
Francisco RomeroUniversidad de Sevilla. [email protected]
PP1
Streamline Topology of Helical Fluid Flow
A vector field with helical symmetry looks the same fromanywhere seen on a specific helix. Helical vector fields areanalysed using dynamical system theory. The helical struc-ture implies existence of a stream function which facilitatesthe analysis. Bifurcation of flow patterns are analysed an-alytically and applied to concrete examples. The resultsare related to vector fields with translational or rotationalsymmetry.
Morten AndersenDepartment of MathematicsTechnical University of [email protected]
PP1
Study of the Connectome of a Simple Spinal CordLocomotor Network.
We address a long-standing ambition of neuroscience tounderstand the structure-function problem by modellingthe complete connectome map of a two-day old hatchlingXenopus tadpole spinal cord based on developmental pro-cesses of axon growth. A simple mathematical model of
228 DS11 Abstracts
axon growth allows us to reconstruct a biologically realisticconnectome of tadpole spinal cord based on the neurobio-logical data (Bristol Xenopus Tadpole Research Lab).Ourstudy reveals a complex structure for the connectome withmany interesting specific features and the distribution ofconnection lengths of the tadpole spinal cord connectomeis found to be similar to that of the global neuronal networkof C. elegans.We use a Hodgkin-Huxley based neuron withpost-inhibitory rebound to model network activity. Thissimple model demonstrates a pattern of neuronal activitywith swimming-like features including left-right alternationand a head-to-tail propagation.
Abul K. Azaduniversity of plymouth, [email protected]
Roman BorisyukUniversity of [email protected]
PP1
Mixed Mode Oscillations in a Gnrh Neuron Model.
Mixed mode oscillations (MMOs) are patterns involvingan inter-mixing of large- and small-amplitude oscillations.For neurons, MMOs are typically mixtures of spikes andsubthreshold oscillations. I will present a model of aGonadotropin-releasing hormone (GnRH) neuron exhibit-ing MMOs, also robustly observed in supporting experi-mental data. I will describe the use of geometric singu-lar perturbation theory methods to understand the mecha-nisms underlying MMOs in the model and explore possiblephysiological functions of MMOs in GnRH neurons.
Sayanti BanerjeeThe Ohio State [email protected]
Janet BestThe Ohio State UniversityDepartment of [email protected]
Kelly SuterThe University of Texas at San [email protected]
PP1
Mixed-Pattern Solutions of An Eighth Order Swift-Hohenberg Equation
Motivated by degenerate marginal stability curves in MHDTaylor-Couette flow, we investigate the existence of mixedpattern solutions for an eighth order Swift-Hohenbergequation. These solutions are analogous to localised so-lutions found in the standard Swift-Hohenberg equation,exhibiting a transition between two patterns of differentwavelengths. A normal form reduction is carried out toidentify regions in the appropriate parameter space wheresuch solutions may occur.
David BentleyUniversity of [email protected]
Alastair M. RucklidgeDepartment of Applied MathematicsUniversity of Leeds
Thomas Wagenknecht, Rainer HollerbachUniversity of [email protected], [email protected]
PP1
An Agent-Based Framework for Designing WaterEfficient Residential Landscapes
I will present an algorithm that uses agent-based modellingand distributed optimization to design water-efficient res-idential landscapes. Agents in this model, which is de-signed to capture the nonlinear relationships between plantgrowth and resource availability, are placed on a simulatedlandscape. The model’s overall dynamics mimic how plantcommunities evolve over time in response to light and wa-ter. Simulation experiments show that this strategy consis-tently produces close-to-optimal solutions, outperformingrandom and greedy search algorithms.
Rhonda HoenigmanUniversity of Colorado, [email protected]
Elizabeth BradleyUniversity of ColoradoDepartment of Computer [email protected]
Nichole BargerUniversity of Colorado, [email protected]
PP1
Migration Effects on Disease Outbreaks
Motivated by the periodic outbreaks of measles in thenorthern and southern regions of Cameroon, we study cou-pled models for the spread of disease in connected subpop-ulations. In the presence of seasonal driving, the couplingis modeled by linear migration or mass action mixing fromsocial interaction. We describe the bifurcations and sensi-tivity in the model to these coupling terms, and show theexistence of different periods of oscillation in each subpop-ulation.
Jackson BurtonMontclair State [email protected]
Lora BillingsMontclair State UniversityDept. of Mathematical [email protected]
Ira B. SchwartzNaval Research LaboratoryNonlinear Dynamical Systems [email protected]
Derek CummingsJohns Hopkins Bloomberg School of Public [email protected]
PP1
Effects of Variability and Noise on Synchrony Be-
DS11 Abstracts 229
tween Reciprocally Pulse Coupled Oscillators withDelays
We analyze two reciprocally pulse-coupled oscillatory neu-rons using Phase Resetting Curves to predict what phase-locked solutions will be exhibited in the neuronal circuitwith conduction delays. We test our predictions in cir-cuits of two model neurons and in hybrid circuits con-structed with two stellate cells constructed via DynamicClamp. Experimental tests confirm our predictions thatthe most robust synchronization for heterogenous neuronsis predicted for long delays with excitatory coupling. Noisepreferentially disrupts early synchrony.
Lakshmi ChandrasekaranNeuroscience centerLouisiana State University Health Sciences [email protected]
Shuoguo WangNeuroscience Center, LSUHSCNew orleans, LA [email protected]
Fernando FernandezDept. of Bioengineering, Brain instituteUniv. of Utah, Salt Lake City, UT [email protected]
John Whitedepartment of BioengineeringThe University of [email protected]
Carmen CanavierHealth Sciences CenterLouisiana State [email protected]
PP1
Exploring the Dynamics of CRISPR Length: HowMuch Can a Bacterium Remember About VirusesThat Infected It?
CRISPR (Clustered Regularly Interspaced Short Palin-dromic Repeats) is a virus-specific heritable bacterial de-fense system that incorporates copies of short regions ofviral DNA into the bacterial genome and grants the bacte-ria immunity to viruses with matching sequences. Ideally,the number of incorporated sequences would grow indef-initely. However, the actual number in any bacteria islimited. We use a birth-death master-equation model toexplore the growth and decay of the CRISPR length.
Lauren M. ChildsCornell [email protected]
Joshua WeitzGeorgia Institute of [email protected]
PP1
Time-dependent Solutions of a Convection Prob-lem with Temperature Dependent Viscosity
We study a convection problem with temperature depen-dent viscosity in a 2D domain with periodic boundary con-
ditions along the horizontal coordinate. Our numerical ap-proach considers the structure of the solutions of the equa-tions in the phase space and its temporal evolution. Thetemporal evolution scheme is similar to the one describedin [I.Mercader, O.Batiste, A.Alonso. An eŒcient spec-tral code for incompressible Æows in cylindrical geometries(2010)]. However, we treat the pressure diœerently, follow-ing the scheme proposed in [H.Herrero, A.M.Mancho. Onpressure boundary conditions for thermoconvective prob-lems (2002)]. Nontrivial stationary solutions are computedvia an iterative Newton-Raphson method.
Jezabel CurbeloInstituto de Ciencias [email protected]
Ana Marıa ManchoInstituto de Ciencias [email protected]
PP1
Correction of Periodic Orbits in High Precision.
We present an algorithm to compute up to any arbitraryprecision periodic orbits of dinamical systems. The algo-rithm is based on an optimized shooting method combinedwith a new numerical ODE solver, TIDES, that uses a Tay-lor series method. This methodology is nowadays the onlyone capable to reach precisions up to 1000 digits or more.Finally, we present some numerical tests for the Henon-Heiles’ Hamiltonian which show the good behavior of theproposed method.
Angeles Dena, Alberto AbadUniversidad de [email protected], [email protected]
Roberto BarrioUniversity of Zaragoza, [email protected]
PP1
Dynamic Switch in a Model of Unfolded ProteinResponse To Endoplasmic Reticulum Stress
The unfolded protein response (UPR) is a cellular mech-anism whose primary functions are to sense perturbationsin the protein-folding capacity and to take corrective stepsrestoring homeostasis. Recent experimental results showthat UPR is capable of producing qualitatively differentoutputs depending on the nature, strength, and persistenceof the inducing stress. In parallel, a mechanistic framework(ODE model) for the integration of stress signals by theUPR has been proposed. We analyze this model and showthe existence of a dynamic switch between two states (anadaptive one and an apoptotic one). The switch matchesthe experimental observations and is a consequence of theintrinsic UPR’s feedback loops.
Danilo Diedrichs, Rodica CurtuUniversity of IowaDepartment of [email protected], [email protected]
PP1
Existence and Stability of Traveling Wave Solutions
230 DS11 Abstracts
in a Simplified Model of Cardiac Tissue.
We introduce a simplified two-variable model of cardiactissue. The model captures key features of cardiac behav-ior, including electrical alternans, while also allowing foranalytical investigations into the propagation of electricalimpulses. We examine the existence and stability of trav-eling wave front and traveling pulse solutions.
Lisa D. Driskell, Gregery BuzzardPurdue [email protected], [email protected]
PP1
Persistence of Normally Hyperbolic Invariant Man-ifolds: The Noncompact Case
We improve the theorem on persistence of Normally Hyper-bolic Invariant Manifolds (NHIMs). The classical theoremsby Fenichel and Hirsch, Pugh & Shub require compactnessof the NHIM, which we generalize to the noncompact case.Furthermore, our results include optimal Ck,α smoothness.To properly generalize to arbitrary manifolds, e.g. withnon-trivial normal bundle, we require the ambient spaceto be a Riemannian manifold of bounded geometry. Weillustrate some of the specific issues in this case.
Jaap ElderingUtrecht [email protected]
PP1
Dimension Reduction of Mechanical Systems
In many applications the governing equations of mechani-cal systems are nonlinear PDEs. These systems are oftentoo complex to be investigated without resorting to numer-ical approximations. A typical property of such approxi-mations is that they are often so high-dimensional thatnumerical bifurcation methods are unlikely to be efficient,which motivates the development of dimension reductionmethods. For a mechanical system we compare the bifur-cation diagrams of the full numerical approximation to itslow-dimensional approximation.
Michael Elmegaard, Jens Starke, Frank SchilderTechnical University of DenmarkDepartment of [email protected], [email protected],[email protected]
Jon J. ThomsenTechnical University of DenmarkDepartment of Mechanical [email protected]
PP1
Frequency Response of Gonadotropin-ReleasingHormone (GnRH) Induced Gonadotropin SubunitTranscription in Pituitary Gonadotrophs
The reproductive system is controlled by a pulsatilegonadotropin-releasing hormone (GnRH) signal. Pituitarygonadotrophs differentially synthesize the beta subunit ofluteinizing hormone (LHβ) or follicle stimulating hormone(FSHβ) in response to variations in the frequency of thissignal. In particular, FSHβ synthesis is preferred at lowGnRH pulse frequencies while LHβ synthesis dominates athigher frequencies. We explore, using mathematical mod-
eling, some potential mechanisms underlying the preferredfrequency response of gonadotropin transcription.
Patrick A. FletcherDepartment of MathematicsFlorida State University, Tallahassee, [email protected]
PP1
Decay and Destruction of Invariant Tori in VolumePreserving Maps
When integrable, the orbits of volume preserving maps lieon invariant tori. While KAM-like theories have shownthe continued existence of these tori under perturbationthere are gaps in our understanding of how these tori be-have when perturbed. In this study 3 dimensional volumepreserving maps with two angles are examined. Numericalresults detailing the resilience of these tori to perturbationwill be discussed, with a focus on finding the last survivingtorus.
Adam M. FoxUniversity of Colorado, [email protected]
James MeissUniversity of [email protected]
PP1
Ergodic and Non-ergodic Clustering of InertialParticles
We compute the fractal dimension of clusters of inertialparticles in mixing flows at finite values of Kubo (Ku) andStokes (St) numbers, by a new series expansion in Ku. Atsmall St, the theory includes clustering by Maxey’s non-ergodic ‘centrifuge’ effect. In the limit of large St and smallKu (so that Ku2St remains finite) it explains clusteringin terms of ergodic ‘multiplicative amplification’. In thislimit, the theory is consistent with the asymptotic pertur-bation series in [Duncan et al., Phys. Rev. Lett. 95 (2005)240602].
Kristian GustafssonGoteborg [email protected]
PP1
Stochastic Network Models of Disease Outbreaks
Regional epidemic data often show fadeouts and reintro-duction of outbreaks of a disease in irregular patterns. Tocapture these dynamics, we construct a network of sub-populations and simulate the disease spread in a finitepopulation. These models are used to analyze the fade-out probabilities with respect to the number of subpopula-tions, connectivity of the network, and the subpopulationsizes. Understanding and enhancing fadeout would facili-tate eradication of the disease.
Jonathan Hayes, Lora BillingsMontclair State [email protected], montclair state university
PP1
Comparison of Different Mean-Field Equations:
DS11 Abstracts 231
Finite-Size Effects and Synchronization
We compare different types of Mean-Field equations forneural networks, either derived from a master-equationformalism, from large-deviations techniques or from a re-cent probabilistic approach. We are particularly interestedin qualitative differences between those approaches. Weparticularly address finite-size effects and synchronizationmechanisms, studied both at the mean-field level via astochastic bifurcation approach, and at the level of a fi-nite network via numerical simulations.
Geoffroy HermannINRIA, [email protected]
Jonathan D. TouboulDepartment of Mathematical PhysicsThe Rockafeller [email protected]
Olivier [email protected]
PP1
Analyzing Point Process Data by Distances andRecurrence Plots
Point process data are difficult to analyze because obser-vations are produced at irregular times while most meth-ods for time series analysis are designed to deal with timeseries with fixed sampling frequencies. In this poster, wepropose a framework for analyzing point process data usingdistances and recurrence plots. First we define distancesbetween point processes. Then recurrence plots can be ap-plied to point processes. We demonstrate the frameworkusing artificial and real datasets.
Yoshito HirataInstitute of Industrial ScienceThe University of [email protected]
Satoshi SuzukiMaster of Financial Engineering Haas School of BusinessUC Berkeleysatoshi [email protected]
Kazuyuki AiharaJST/University of Tokyo, JapanDept of Mathematical [email protected]
PP1
Analysis of the Shimmy Phenomenon in AircraftMain Landing Gears
Nonlinear equations of motion are developed for a two-wheeled main landing gear of a mid-size passenger aircraft.They allow us to perform a bifurcation study of the occur-rence of different types of shimmy oscillations, dependenton the forward velocity V and the vertical force Fz actingon the gear. Changes to the bifurcation diagram in the(V,Fz)-plane on design parameters are also considered.
Chris HowcroftUniversity of [email protected]
PP1
Adaptive Mathematical Model of Heat and MassTransfer for Automatic Control of Solidification inContinuous Casting
Model based predictive (MBP) control is the most effec-tive way of automatic process control in continuous casting.For its design it is necessary to create an adaptive mathe-matical model that will accurately reproduce the real pro-cess. Research methodologies are based on the equationsof mathematical physics, the theory of inverse problems foridentification of distributed parameter, control theory andcomputer modeling techniques.
Ganna IvanovaIAMM [email protected]
PP1
Fronts and Pulses Locked to Stimuli in ContinuumNeuronal Networks
In continuum neuronal networks modeled by integro-differential equations, we investigate the existence of trav-eling waves. We show stimulus-locked fronts exist on aspecific interval of stimulus speeds for a scalar field modelwith a general firing rate function and spatio-temporallyvarying stimulus. After adding a slow adaptation equa-tion, we obtain a formula, involving an adjoint solution,for stimulus speeds that induce locked pulses. Analyticallycomputed bounds for stimulus-locked waves are comparedto numerical simulations.
Jozsi Z. JalicsDepartment of Mathematics and StatisticsYoungstown State [email protected]
Bard Ermentrout, Jonathan E. RubinUniversity of PittsburghDepartment of [email protected], [email protected]
PP1
Linear Conjugacy of Chemical Reaction Networks
Under suitable assumptions, the dynamic behaviour of achemical reaction network is governed by an autonomousset of polynomial ordinary differential equations over con-tinuous variables representing the concentrations of the re-actant species. It is known that two networks may pos-sess the same governing mass-action dynamics despite dis-parate network structure. To date, however, there has onlybeen limited work exploiting this phenomenon even for thecases where one network possesses known dynamics whilethe other does not. We bring these known results into abroader unified theory which we call conjugate chemical re-action network theory. We present a theorem which givesconditions under which two networks with different govern-ing mass-action dynamics may exhibit the same qualitativedynamics and use it to extend the scope of the well-knowntheory of weakly reversible systems.
Matthew D. Johnston, David SiegelUniversity of [email protected], [email protected]
232 DS11 Abstracts
PP1
Delay Coupled Limit Cycle Oscillators with Non-Linear Frequency Shift Effects
We study nonlinear frequency shift effects on the collectivedynamics of two limit cycle oscillators near Hopf bifurca-tion coupled with time delay. A minimal oscillator modelthat includes non-linear frequency shift effects is obtainedby averaging over the fast periodic behavior of the Van derPol Duffing equation.
George L. JohnstonEduTron [email protected]
Abhay RamPlasma Science and Fusion Center, M.I.T.Cambridge, MA 02139 [email protected]
Abhijit SenInstitute for Plasma ResearchBhat, Gandhinagar 382428, [email protected], [email protected]
PP1
Linearization of Hyperbolic Finite-Time Processes
We adapt the notion of processes to introduce an abstractframework for finite-time dynamics, e.g. ODEs on compacttime-intervals. For linear finite-time processes a notion ofhyperbolicity namely exponential monotonicity dichotomy(EMD) is introduced, thereby generalizing and unifyingseveral existing approaches. We present a spectral theoryfor linear processes, prove robustness of EMD and provideexact perturbation bounds. We investigate linearizationsof nonlinear processes and show finite-time analogoues ofthe local (un)stable manifold theorem and theorem of lin-earized asymptotic stability.
Daniel KarraschTechnische Universitat DresdenInstitute of [email protected]
PP1
Transferring Time Series Analysis Methods toPoint Processes
The analysis of dynamical systems received much attentionover the past decades. In particular, there is a strong focuson the analysis of time series generated by dynamical pro-cesses. A second class of processes the so-called point pro-cesses in times received much less attention although suchprocesses occur in physical, biological and many other ap-plications. Here, we focus on the spectral analysis of pointprocesses and discuss its abilities and limitations.
Malenka KillmannFreiburg Center for Data Analysis and ModelingUniversity of Freiburg, Physical [email protected]
Linda SommerladeFreiburg Center for Data Analysis and ModelingUniversity of [email protected]
Wolfgang Mader
Freiburg Center for Data Analysis and Modeling,UniversityDepartment of Physics, University of [email protected]
Jens TimmerUniversity of FreiburgDepartment of [email protected]
Bjorn SchelterFreiburg Center for Data Analysis and ModelingUniversity of [email protected]
PP1
Clustering Generates Gamma Rhythms in a Re-current Neuronal Network with Spike FrequencyAdaptation
We study a model network of spiking neurons with spikefrequency adaptation globally coupled with recurrent inhi-bition. Population activity organizes into a high frequencyrhythm (20-80Hz). Using singular perturbation theory, weapproximate the spiking frequency of an individual neu-ron to be moderate (5-10Hz), compared to the populationgamma rhythm. The network forms clusters of neuronsand each cluster spikes out of phase with the others, asplay state. We find that we can solve exactly for the pe-riodic solution of an individual neuron and its associatephase response curve (PRC). Using the PRC, we analyti-cally predict the number of clusters in the splay state usinglinear stability analysis of the incoherent state.
Zachary KilpatrickUniversity of [email protected]
Bard ErmentroutUniversity of PittsburghDepartment of [email protected]
PP1
Mixed Mode Oscillations and Graded PersistentActivity Contribute to Memory Formation
Neurons in layer V of the entorhinal cortex play a crucialrole in memory formation, and these neurons have verydistinctive activity including mixed mode oscillations andgraded persistent activity. In order to understand howthese characteristic firing patterns may interact function-ally in memory formation, we use bifurcation theory to an-alyze a 6-dimensional reduction from a conductance-basedmathematical model of a layer V neuron. We discuss theionic mechanisms involved and the implications for mem-ory.
Jung Eun KimDepartment of MathematicsThe Ohio State [email protected]
Janet BestThe Ohio State UniversityDepartment of [email protected]
DS11 Abstracts 233
PP1
Intrinsic Localized Modes in Mechanically CoupledCantilever Array with Tunable On-Site Potential
A macro-mechanical cantilever array is proposed for exper-imental manipulation of intrinsic localized mode (ILM).The array consists of cantilevers, electromagnets facedon the cantilevers, elastic rods for coupling between can-tilevers, and a voice coil motor for external excitation. Anonlinearity in the restoring force of cantilever appears dueto the magnetic interaction. Several ILMs were successfullygenerated by the sinusoidal excitation. The experimentalobservations and manipulations will be reported in detail.
Masayuki KimuraSchool of EngineeringThe University of Shiga [email protected]
Takashi HikiharaKyoto UniversityDepartment of Electrical [email protected]
PP1
Linear Response Prediction for Fluctuation-Dissipation With Adaptive Time Stepping
The fluctuation-dissipation theorem has inspired much re-search in statistical physics, since it provides a means foranalyzing response to external forcing of a dynamical sys-tem in statistical equilibrium. We present an algorithmto predict average linear response to small perturbationsin forcing for chaotic nonlinear dynamical systems. Addi-tionally, we implement an adaptive time stepping methodto significantly improve computational efficiency.
Marc KjerlandUniversity of Illinois at [email protected]
Rafail AbramovDepartment of Mathematics, Statistics and ComputerScienceUniversity of Illinois at [email protected]
PP1
Amplitude Equations for SPDEs with Cubic Non-linearities on Unbounded Domains
The evolution of modulated patterns for SPDEs on un-bounded domains near a change of stability is described byamplitude equations. Under appropriate scaling solutionsare approximated by periodic waves modulated by solu-tions to a stochastic Ginzburg-Landau equation. The goalis to derive rigorous error estimates. Typical examples arethe Swift-Hohenberg equation, a model arising in surfacegrowth, and Rayleigh-Benard convection. This research isbased on results by Blomker, Hairer, and Pavliotis.
Konrad KlepelUniversitat [email protected]
PP1
Numerical Continuation Applied to Landing Gear
Mechanism Analysis
The landing gears of an aircraft need to deploy reliably inall operating conditions. A method is presented to deriveequilibrium equations along with equations describing thegeometric constraints in the mechanism. This modellingapproach is efficient and flexible because it allows one tocontinue solutions numerically in any of the parametersof interest. The method is applied to a nose landing gear,which is a planar mechanism, and a main landing gear witha side-stay, which is an example of a mechanism in threedimensions.
James KnowlesUoB PhD [email protected]
Bernd KrauskopfUniversity of BristolDepartment of Engineering [email protected]
Mark LowenbergDept. of Aerospace EngineeringUniversity of [email protected]
PP1
Spatiotemporal Ecology by Remote Sensing fromSatellite Imagery
Plankton blooms severely impact coastal regions. Wemodel this ecology as informed by remote sensing. We inferflow fields from satellite imagery by inverse problem tech-niques. We analyze transport in resulting vector fields byfinite-time Lyapunov Exponents and the Frobenius-Perrontransfer operator, revealing psuedo-barriers in the flow.Global modeling methods for the population dynamic re-action diffusion advection systems will also be discussed.
Sean Kramer, Ranil Basnayake, Erik BolltClarkson [email protected], [email protected],[email protected]
Aaron B. LuttmanClarkson UniversityDepartment of [email protected]
PP1
Sliding Mode Control Applied to SuppressGrazing-Induced Chaos in An Impact Oscillator
Previous works showed that a simple soft impact oscillatorin certain parameter region exhibits narrow band of chaosnear grazing. This work explores the possibility of apply-ing nonlinear control method to avoid the occurrence ofchaos and ensure trajectory tracking in that parameter re-gion. We have used input-output feedback linearization tolinearize the nonlinear control law and designed a slidingmode controller based on the feedback linearized system.The control law was verified in presence of parameter un-certainty.
Soumya KunduElectrical Engineering and Computer ScienceUniversity of Michigan, Ann Arbor, USA
234 DS11 Abstracts
PP1
Stochastic Synchronization of Neuronal Popula-tions with Intrinsic and Extrinsic Noise
We extend the theory of noise-induced phase synchroniza-tion to the case of a neural master equation describingthe stochastic dynamics of interacting excitatory and in-hibitory populations of neurons (E-I networks). Assumingthat each deterministic E-I network acts as a limit cycle os-cillator, we combine phase reduction and averaging meth-ods in order to determine the stationary distribution ofphase differences in an ensemble of uncoupled E-I oscilla-tors, and use this to explore how intrinsic noise disruptssynchronization due to a common extrinsic noise source.
Yi Ming LaiUniversity of [email protected]
Paul C. BressloffUniversity of Utah and University of Oxford, UKDepartment of [email protected]
PP1
Mathematical Modeling of Hydrodynamic Contri-butions to Amoeboid Cell Motility
Understanding the methods by which cells move is a fun-damental problem in modern biology. Recent evidence hasshown that the fluid dynamics of cytoplasm can play avital role in cellular motility. The slime mold Physarumpolycephalum provides an excellent model organism for thestudy of amoeboid motion. In this research, we numeri-cally investigate intracellular fluid flow in a simple modelof Physarum. The Immersed Boundary Method is used toaccount for the forces generated by the cytoplasmic flow.We investigate the relationship between contraction waves,flow waves and locomotive forces, and characterize condi-tions necessary to generate directed motion.
Owen LewisUniversity of California, [email protected]
Robert D. GuyMathematics DepartmentUniversity of California [email protected]
PP1
From Synchronous Oscillations to Oscillation-arrested for Segmentation Clock Gene of Zebrafish
Somitogenesis observed in the vertebrate embryos is a pro-cess for the development of somites. The pattern of somitesis traced out by the segmentation clock genes which un-dergo synchronous oscillation and the oscillation-arrestedas the embryo grows. We consider a model on zebrafishsegmentation clock-genes with time delay and obtain an-alytic methods to derive the oscillation-arrested, and theexistence and the stability of the synchronous oscillation.
Kang-Ling Liao, Chih-Wen ShihNational Chiao Tung [email protected], [email protected]
PP1
Interaction of Epidemic and Information Spreadingin Adaptive Networks
We model simultaneous spreading of an epidemic and in-formation about the epidemic on an adaptive social net-work. Information is interpreted as awareness of the needto practice disease avoidance behavior by rewiring onesnetwork connections. The effects of external informationsources (e.g., media) and node-to-node communication areexplored, and stochastic simulations are compared with amoment closure approximation. Network adaptation gen-erates periodic oscillations for certain ranges of parameters.
Yunhan LongCollege of William and [email protected]
Thilo GrossMPI for the Physics of Complex [email protected]
Leah ShawThe College of William & [email protected]
PP1
From Bivariate Analysis to the Small World Prop-erty
Networks are omnipresent with applications ranging fromtraffic to social to neural networks. The small world prop-erty, defined by the cluster coefficient and the averageshortest pathlength, charcterizes certain aspects of a net-work. The local cluster coefficient measures the local den-sity of the network. We demonstrate that it is artificiallyincreased by using ordinary bivariate analysis techniques.We discuss the influence of such bivariate analysis tech-niques and thresholding on the conclusion towards smallworld property.
Wolfgang MaderFreiburg Center for Data Analysis and Modeling,UniversityDepartment of Physics, University of [email protected]
Malenka KillmannFreiburg Center for Data Analysis and ModelingUniversity of Freiburg, Physical [email protected]
Linda SommerladeFreiburg Center for Data Analysis and ModelingUniversity of [email protected]
Jens TimmerUniversity of FreiburgDepartment of [email protected]
Bjorn SchelterFreiburg Center for Data Analysis and ModelingUniversity of [email protected]
DS11 Abstracts 235
PP1
Reducing the Dimension of Mathematical Modelsof Physiological Systems
Detailed physiological models can contain large numbers ofvariables, making analysis difficult. Various ad hoc meth-ods are commonly used to reduce the dimension of thesemodels, with the aim being to capture the essential dy-namics in a reduced system which is easier to analyze. Inthis poster, we study common methods of reducing the di-mension of the Hodgkin-Huxley equations; we apply thesemethods, in a mathematically rigorous manner to a specificneural model.
Pingyu NanUniversity of [email protected]
PP1
Hybrid Deterministic/stochastic Processes andOptimal Search Strategies
A model of an intermittent random search in a two dimen-sional domain is formulated to study cellular transport ofmRNA. A particle moves deterministically (i.e. no Brow-nian motion) with a velocity that randomly jumps at ex-ponentially distributed time intervals. We show how themean first passage time to a small target can be optimizedby tuning the parameters that influence the random veloc-ity jumps.
Jay M. NewbyUniversity of OxfordMathematical [email protected]
Paul C. BressloffUniversity of Utah and University of Oxford, UKDepartment of [email protected]
PP1
Discovering Novel Treatment Strategies for Type 1Diabetes Through Mathematical Modeling
We provide a bifurcation analysis of a mathematical modelfor the early stages of type 1 diabetes in the diabetesprone NOD mouse, using the phagocytosis rates of rest-ing and activated macrophages as bifurcation parameters.The model parameters are based on data available in theliterature and estimates based on knowledge of intercellulardynamics in mice. We conclude our analysis by proposing4 model-guided, novel treatment strategies, one of whichseems contra intuitive at first glance. Furthermore we in-vite the medical community to perform straight forwardexperiments to test our findings.
Kenneth Hagde M. NielsenRoskilde [email protected]
Johnny T. OttesenRoskilde UniversityDepartment of [email protected]
PP1
Reconstructing Neuronal Inputs from Voltage
Recordings
Reconstructing stimulus-evoked temporally-varying inputto a neuron in vivo is challenging. The existing model-based method allows the resolution of two synaptic con-ductances corresponding to two distinct reversal potentials.We present a new approach enabling the reconstruction ofthree input conductances. Our method is based on treatingsynaptic conductances and membrane voltage as randomvariables and deriving equations for both first and secondmoments. We apply reconstruction to simulated data anddiscuss applicability to experimental data.
Stephen E. OdomUniversity of [email protected]
Alla BorisyukUniversity of UtahDept of [email protected]
PP1
Phase Reduction for Analyzing Collective Rhythmsof Delay-Induced Oscillations
Delay-induced oscillations and their interactions play es-sential roles in many biological systems, such as electro-encephalogram (EEG) activities and genetic oscillations.In analyzing oscillation systems, the phase reductionmethod is known to be quite useful. However, it has notbeen fully utilized in analyzing models of coupled delay-induced oscillations, because of their infinite-dimensionalnature. In this study, we apply phase reduction to thecoupled delay-induced oscillations and analyze nontrivialcollective rhythms.
Yutaro Ogawa, Ikuhiro YamaguchiGraduate School of Frontier SciencesThe University of [email protected], [email protected]
Hiroya NakaoDepartment of PhysicsKyoto [email protected]
Yashuhiko JimboGraduate School of Frontier SciencesThe University of [email protected]
Kiyoshi KotaniGraduate School of Frontier Science,The University of [email protected]
PP1
One Possible Mechanism Underlying Intermit-tently Synchronous Activity Patterns.
Abnormally synchronous oscillations in basal ganglia ofParkinsonian patients are characterized by frequent andirregular interruption through short-lived desynchroniz-ing events. In this study, we investigated one possiblegeneric mechanism using simple network.We used geomet-ric dynamical systems methods for analysis. Our resultdemonstrates that intermittently synchronous oscillationsare generated by overlapped spiking which crucially depend
236 DS11 Abstracts
on the geometry of slow phase plane and the interplay be-tween slow variables as well as the strength of synapses.
Choongseok Park, Leonid RubchinskyDepartment of Mathematical SciencesIndiana University Purdue University [email protected], [email protected]
PP1
Symmetry Breaking Bifurcations in a D4 Symmet-ric Hamiltonian System
We investigate a numerical method to locate periodic or-bits in Hamiltonian systems of two degrees of freedom in aD4 and time reversal symmetric Hamiltonian. The proce-dure to obtain the “skeleton’ of periodic orbits consist ofa combination of several methods. The combination of allthe techniques is used to provide a complete study of sym-metry breaking bifurcations in a particular Hamiltoniansystem that has D4 and time reversal symmetry.
Slawomir PiaseckiThe University of [email protected]
Roberto BarrioUniversity of Zaragoza, [email protected]
Fernando BlesaUniversity of [email protected]
PP1
Optimal Trajectories, Front Tracking, and La-grangian Structures in Coastal Ocean Flows
The Lagrangian particle viewpoint is crucial for the anal-ysis and observation of oceanographic flows. It is alsouseful for determining optimal trajectories for underwaterautonomous vehicles, especially in the presence of strong,time-varying currents. We solve the Hamilton Jacobi Bell-man equation indirectly via the extremal field approachwhich we relate to front tracking for minimum time/energycontrol in the Adriatic Sea, relating the results to La-grangian structures in the flow field.
Blane RhoadsUniversity of California Santa [email protected]
Igor MezicUniversity of California, Santa [email protected]
Andrew PojeMathematicsCUNY-Staten [email protected]
PP1
Mode Interactions Between Superlattice Patterns.
Pattern selection in the Faraday wave experiment is under-stood by using three-wave interactions. We focus on thebicritical point where two instabilities with different wave-lengths occur together. We consider a wavelength ratio
of√
7 associated with 22◦ superhexagons, with a super-hexagonal lattice in one mode and a hexagonal lattice inthe other. We show the stability regions of the various pat-terns and compare solutions between the amplitude equa-tions and a model PDE.
Pakwan RiyapanUniversity of [email protected]
Alastair M. RucklidgeDepartment of Applied MathematicsUniversity of [email protected]
PP1
Riemann Problems for Multiphase Flow with Sev-eral Thermodynamic Equilibria.
We study the Riemann problem for a system of hyperbolicconservation laws modeling multiphase fluid flow involvingdistinct thermodynamic equilibria. Such models imposesevere obstructions on the solution of the Riemann prob-lem due to failure of strict hyperbolicity: even existenceand admissibility became thorny issues. Our applicationis the injection of a volatile alkane into a porous mediumunder local thermodynamical equilibrium, except at verylocalized places.
Julio Daniel M. SilvaInstituto Nacional de Matematica Pura e AplicadaE. Dona Castorina 110, 22460-32, Rio de Janeiro, RJ [email protected]
Dan MarchesinInstituto Nacional de Matematica Pura e [email protected]
PP1
Modelling Gang Membership in Trinidad and To-bago As An Epidemic
Techniques developed for the modelling of infectious dis-eases and epidemics in a population are applied to studythe growth of gangs. A criminal gang is treated as an in-fection that spreads by interactions among gang membersand others in the population. We develop a mathematicalmodel consisting of a system of coupled ordinary differen-tial equations to describe how gang membership changesover time and explore strategies to reduce the spread ofgangs.
Joanna Sooknanan, Balswaroop Bhatt, Donna ComissiongUniversity of the West [email protected], [email protected],[email protected]
PP1
The Effect of Network Structure on the Path toSynchronization in Large Systems of Coupled Os-cillators
We employ the Kuramoto Model to study how differentnetwork parameters influence the dynamics of large sys-tems of coupled oscillators. In particular, we investigatethe effects that network topology, natural frequency dis-tribution, and the number of oscillators have on the path
DS11 Abstracts 237
these systems take towards global synchronization as theoverall coupling strength between oscillators is increased.
John E. StoutDepartment of PhysicsNorth Carolina State [email protected]
Matthew WhitewayDepartment of Physics and AstronomyUniversity of [email protected]
Edward OttUniversity of MarylandInst. for Plasma [email protected]
Michelle GirvanUniversity of [email protected]
Thomas AntonsenInstitute for Research in Electronics and Applied PhysicsUniversity of [email protected]
PP1
Dynamics of Actuators and Actuator Arrays
Various actuators (DC motors, pneumatics, bimetallicstrips, etc.) have been explored as elements of coupledarrays. The goal is to find useful self-organized patterns inthe coupled systems. A particularly simple actuator choiceis a bimetallic buckled beam, which is used to make a heatengine cycling between a heat source and heat sink. An-other choice is a pneumatic piston, which is used in anarray of muscles for a robotic horse.
Randall TaggUniversity of Colorado [email protected]
Vinnie BasileWestminster High SchoolColoradovinnie [email protected]
Rod CruzKearney Middle School / Adams [email protected]
PP1
Real-Valued Complex Chaotic Spreading Se-quences with Constant Power in Complex CDMA
We evaluate performance of complex CDMA using real-valued complex chaotic spreading sequences with constantpower. Usually, tight power control is necessary for real-valued chaotic signal to be used in communication sys-tem. However, the chaotic sequences used here realizeconstant power. Since an exact invariant measure of thesequences can be obtained, the signal-to-interference ratioof the chaotic sequences in chip-synchronous CDMA canbe obtained analytically. Additionally, several interesting
properties of the sequences will be shown.
Ryo TakahashiDepartment of Electrical Engineering,Graduate School of Engineering, Kyoto [email protected]
PP1
Blowup Solutions of the Korteweg-De Vries Equa-tion
We study blowup solutions of the generalized Korteweg-deVries equation (GKdV). These solutions arise when a soli-ton turns unstable and then becomes infinite in finite time;in other words blow up. Through a dynamical rescaling wereduce the GkdV to an ODE. Then, we use asymptoticmethods and matching techniques to construct boundedsolutions of the ODE. Moreover, with the asymptotic anal-ysis we determine the parameter range over which thesesolutions may exist.
Vincent TimperioUniversity of [email protected]
Vivi RottschaferDepartment of MathematicsLeiden [email protected]
PP1
Synchronization of Stochastic Oscillators
We consider finite state Markov jump processes with timedependent perturbations of the transition rates. Sucha model, for instance, describes the stochastic cycles ofconfiguration changes in enzymes or molecular motors.Through the time dependence of the transition rates thesestochastic oscillations can be coupled to other oscillatorsor subjected to time periodic pumping. Here we study theeffect of such coupling on the frequency and the coherenceof the stochastic oscillators. Nonlinear effects in the vicin-ity of resonant frequencies are discussed as synchronizationphenomena.
Ralf ToenjesOchanomizu University,Ochadai Academic [email protected]
PP1
Pulses in Singularly Perturbed Two ComponentReaction-Diffusion Equations
Recently, methods have been developed to study the ex-istence and stability of pulses in singularly perturbed sys-tems of reaction-diffusion equations in one spatial dimen-sion. The context of model problems (Gray-Scott, Gierer-Meinhardt) in which these methods were developed has hadan influence on the applicability of the latter: the charac-teristics of these model problems was crucially used. In thisposter, we present an extended explicit theory for pulsesin two component singularly perturbed reaction-diffusionequations in a general setting.
Arjen DoelmanUniversity of [email protected]
238 DS11 Abstracts
Frits VeermanMathematical InstituteLeiden [email protected]
PP1
An Analytical Method to Compute BifurcationCurves for Neural Networks with Space DependentDelays
We study neural networks with space dependent delays:these delays arise from the synaptic time integration (con-stant part of the delays) and from the propagation time ofthe signal (which is space dependent). Delayed neural net-works analysis is both difficult at the theoretical level andat the numerical level. In particular, the analysis of thelinear stability of stationary solutions which relies on thecomputation of the eigenvalues of the linearized equationis very time consuming. Based on an analytical formulafor the rightmost eigenvalue, we are able to explain therole of constant delays versus space-dependent delays forarbitrary connectivity. Numerical examples are provided.
Romain VeltzINRIA [email protected]
PP1
Mathematical Modelling of Membrane Separation
Membrane separation is commonly used in chemistry andchemical engineering, where the separation of one or sev-eral species of molecules is of interest. This presentationwill presents mathematical modelling of the dynamic in-terplay between the transport equations through the mem-brane and the transport equations within the bulk solution.Thus, resulting in a system of coupled ODE’s and PDE’swith time varying boundary conditions. The model is usedfor predicting optimal parameters for separation processes.
Frank VintherDepartment of MathematicsTechnical University of [email protected]
PP1
Pattern Formation on Small World Networks
The Turing instability is a classic mechanism for the forma-tion of spatial structures in non-equilibrium systems andhas recently been investigated by Nakao and Mikhailovin the context of complex networks. We continue thesestudies and analyze stationary and oscillatory patterns inreaction-diffusion systems on small-world networks. Weparticularly discuss how the observed patterns are affected,if the network is rewired randomly. Extensions to 2D mod-els are presented.
Thomas WagenknechtUniversity of [email protected]
Nick McCullenSchool of MathematicsUniversity of [email protected]
PP1
Rigid Phase Shifts in Periodic Solutions of NetworkSystems and Network Symmetry
It is well known that the dynamics of a network systemis constrained by its structure. So the network structuremight be inferred from its dynamics. In this poster, wepresent a suprising result concerning the relationship be-tween phase patterns of periodic solutions (a phase patterndefined by phase relations of the nodes on the network)and network symmetries. We show that if the phase pat-tern of a hyperbolic periodic solution persists under smallperturbations, then a quotient network that is obtained byidentifying synchronous nodes must possess symmetries.
Yunjiao WangOhio State [email protected]
PP1
Slow Variable Dominance in Beta-Cell Models
Bursting oscillations are common in neurons and endocrinecells. One type of bursting model with two slow variablesproduces ‘phantom bursting’ in which the burst period isdetermined by a blend of the time constants of the slowvariables. We define a measure, the ‘dominance factor’, ofthe relative contributions of the slow variables and apply itto the bursting produced by biophysical phantom burstingmodels. We show that the dominance factor is a useful toolfor understanding the slow dynamics that underlie phan-tom bursting oscillations.
Margaret A. WattsDeptment of MathematicsFlorida State [email protected]
Joel TabakDept of Biological SciencesFlorida State [email protected]
Richard BertramDepartment of MathematicsFlorida State [email protected]
PP1
Traveling Waves in a Neural Field Model of Binoc-ular Rivalry
We analyze traveling wave solutions in a neural field modelof binocular rivalry. We consider two one-dimensional ex-citatory networks with slow synaptic depression that mu-tually inhibit each other. Using a slow/fast manifold de-composition, we show how the depression of excitatorysynapses in the network corresponding to the dominanteye breaks a left/right eye exchange symmetry, allowing forthe propagation of a traveling front solution. The latter ischaracterized by a retreating activity front in the dominanteye population and an advancing front in the suppressedeye population. We calculate how the speed of the frontdepends on various physiological parameters, and compareour results with recent experimental studies of binocularrivalry waves.
Matthew WebberMathematical Institute
DS11 Abstracts 239
University of [email protected]
Paul C. BressloffUniversity of Utah and University of Oxford, UKDepartment of [email protected]
PP1
Spiral Defect Chaos and Skew-Varicose Instabilityof 2D Generalized Swift-Hohenberg Model Equa-tions.
Spiral defect chaos (SDC), observed in Rayleigh-Benardconvection, is studied numerically in generalized Swift-Hohenberg models with mean flow. We compare analyticaland numerical results to study the linear stability of rolls.With mean flow, rolls are unstable to skew-varicose insta-bility (SVI) and the boundary is calculated. We establishthe relation between SVI and SDC. Asymptotic behavioursof SVI is analyzed. The region of stable rolls for long wave-length instabilities is modified to include cross-rolls insta-bility.
Jinendrika A. WeliwitaUniversity of [email protected]
Alastair M. RucklidgeDepartment of Applied MathematicsUniversity of [email protected]
Steve TobiasUniversity of [email protected]
PP1
An Equationless Approach to Studying the Orga-nizing Principles of a Multifunctional Central Pat-tern Generator
We describe a novel computational approach to reduce de-tailed models of central pattern generation to an equa-tionless mapping that can be studied geometrically. Ouranalysis does not require knowledge of the equations thatmodel the system, and provides a powerful new approachto studying detailed models. We demonstrate on a motif ofthree reciprocally inhibitory cells, able to produce multiplebursting rhythms. multistability and the types of attrac-tors in the network are shown to be determined by the dutycycle of bursting.
Jeremy WojcikGeorgia State UniversityDept. Mathematics and [email protected]
Andrey ShilnikovNeuroscience Institute and Department of MathematicsGeorgia State [email protected]
Robert ClewleyDepartment of Mathematics and StatisticsGeorgia State University
PP1
Phase-Locking in Chains of Half-Center Oscilla-tors: Mechanisms Underlying Phase Constancy inthe Crayfish Swimmeret System
The basic central-pattern generating unit of the crayfishswimmeret system is the so-called half-center oscillator,which is composed of two cells coupled by inhibition.We use the phase response curves of these oscillators, inconjunction with symmetry arguments and the theory ofweakly coupled oscillators, to assess the ability of differentconnectivity schemes of a chain of oscillators to producethe appropriate 25% phase constancy observed in crayfishswimming.
Jiawei ZhangGraduate Group in Applied MathematicsUniversity of California, [email protected]
Timothy LewisDepartment of MathematicsUniversity of California, [email protected]
PP1
Augmented Graph Method for Synchronization inDirected Networks
We extend the generalized connection graph method forsynchronization in directed networks. The new componentof the method is the use of the symmetrize-weight-and-augment operation. This amounts to replacing each directlink between node i node j by an undirected edge witha coupling strength that depends on the node unbalancebetween the two nodes. This quantity is defined to be thedifference between the sum of connection coefficients of theoutgoing edges and the sum of the connection coefficientsof the incoming edges to the node. In addition, we augmentthe graph by adding an extra edge, connecting node i andnode j if their mean node unbalance is negative. Differentweights are also associated with each path between any twonodes of the augmented undirected network, according tothe mean node unbalance. The synchronization criterionfor this augmented symmetrized network also guaranteesglobal stability of synchronization in the original directednetwork. We show that the new augmented graph methodis more effective than the original connection graph forproving synchronization in sparse directed networks.
Ken ZhaoGeorgia State [email protected]
Igor BelykhDepartment of Mathematics and StatisticsGeorgia State [email protected]
PP1
Cardiac Disease Detection by Mostly Conjugacy
Mostly conjugacy is a technique which compares dynam-ical systems, in a way of judging the quality of matchingby looking at their topological difference (homeomorphicdefect). We applied this technique to regular physical ex-
240 DS11 Abstracts
amination of heart. By studying homeomorphic defect be-tween data of examinations, we can detect large changes ofcardiac health, i.e. from healthy heart to unhealthy heart,and distinguish it to minor changes, such as measurementnoise, small physical condition variance between examina-tions.
Jiongxuan ZhengClarkson [email protected]
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