Anti-Synchronization of Chaotic Systems via Adaptive Sliding Mode Control

A Series Journal of the Chinese Physical SocietyDistributed by IOP Publishing

Online: http://iopscience.iop.org/cplhttp://cpl.iphy.ac.cn

C H I N E S E P H Y S I C A L S O C I E T Y

ISSN: 0256-307X

中国物理快报

ChinesePhysicsLettersVolume 29 Number 12 December 2012

CHIN.PHYS. LETT. Vol. 29, No. 12 (2012) 120505

Anti-Synchronization of Chaotic Systems via Adaptive Sliding Mode Control *

Wafaa Jawaada1, M. S. M. Noorani1, M. Mossa Al-sawalha21School of Mathematical Sciences, Universiti Kebangsaan Malaysia,

43600 UKM Bangi, Selangor, Malaysia2Faculty of Science, Mathematics Department, University of Hail, Kingdom of Saudi Arabia

(Received 18 April 2012)An anti-synchronization scheme is proposed to achieve the anti-synchronization behavior between chaotic systemswith fully unknown parameters. A sliding surface and an adaptive sliding mode controller are designed to gainthe anti-synchronization. The stability of the error dynamics is proven theoretically using the Lyapunov stabilitytheory. Finally numerical results are presented to justify the theoretical analysis.

PACS: 05.45.−a, 47.52.+j, 89.75.−k DOI: 10.1088/0256-307X/29/12/120505

One of the most important aspects of nonlineardynamical systems is the property of synchronizationor anti-synchronization, which classically representsthe entrainment of frequencies of oscillations due toweak interactions. Studies in this field have led tovarious definitions and techniques for the analysis ofthis property. This is generally due to its prospectiveapplications especially in chemical reactions, powerconverters, biological systems, information process-ing and secure communications.[1−3] A wide varietyof approaches have been proposed for the synchro-nization or anti-synchronization of chaotic systems,which include generalized active control,[4−6] nonlin-ear control,[7,8] adaptive control[9,10] and sliding modecontrol.[11,12] Fortunately, some existing methods ofsynchronizing can be generalized to anti-synchronizechaotic systems. However, in practical engineering sit-uations, parameters are probably unknown and maychange from time to time. Therefore, there is a vi-tal need to effectively anti-synchronize two chaoticsystems (identical and different) with unknown pa-rameters. This is typically important in theoreticalresearch as well as practical applications. Amongthe aforementioned methods, adaptive sliding modecontrol is an effective option for achieving the anti-synchronization of chaotic systems with fully unknownparameters. To formulate the anti-synchronizationproblem of the chaotic system via adaptive slidingmode control, we consider the drive chaotic systemin the form

�� = 𝑓(𝑥) + 𝐹 (𝑥)𝛼, (1)

where 𝑥 ∈ Ω1 ⊂ 𝑅𝑛 is the state vector, 𝛼 ∈ 𝑅𝑚 isthe unknown parameter vector of the system, 𝑓(𝑥) isan 𝑛 × 1 matrix, 𝐹 (𝑥) is an 𝑛 × 𝑚 matrix and theelements 𝐹𝑖𝑗(𝑥) in matrix 𝐹 (𝑥) satisfy 𝐹𝑖𝑗(𝑥) ∈ 𝐿∞for 𝑥 ∈ Ω1 ⊂ 𝑅𝑛. On the other hand, the responsesystem is assumed by

�� = 𝑔(𝑦) +𝐺(𝑦)𝛽 + 𝑢(𝑡), (2)

where 𝑦 ∈ Ω2 ⊂ 𝑅𝑛 is the state vector, 𝛽 ∈ 𝑅𝑞 is theunknown parameter vector of the system, 𝑔(𝑦) is an

𝑛 × 1 matrix, 𝐺(𝑦) is an 𝑛 × 𝑞, 𝑢(𝑡) ∈ 𝑅𝑛 is controlinput vector, and the elements 𝐺𝑖𝑗(𝑦) in matrix 𝐺(𝑦)satisfy 𝐺𝑖𝑗(𝑦) ∈ 𝐿∞ for 𝑦 ∈ Ω2 ⊂ 𝑅𝑛. If system (1)and system (2) satisfy 𝑓(·) = 𝑔(·) and 𝐹 (·) = 𝐺(·),then the structures of system (1) and system (2) areidentical. Otherwise, the two systems will be differ-ent. Let 𝑒 = 𝑦 + 𝑥 be the anti-synchronization errorvector. Our goal is to design a controller 𝑢 such thatthe trajectory of the response system (2) with initialcondition 𝑦0 can asymptotically approach the drivesystem (1) with initial condition 𝑥0 and finally imple-ment the anti-synchronization such that

lim𝑡→∞

‖𝑒‖ = lim𝑡→∞

‖𝑦(𝑡, 𝑦0) + 𝑥(𝑡, 𝑥0)‖ = 0, (3)

where ‖ · ‖ is the Euclidean norm. The sliding modecontrol method of anti-synchronization involves twomajor stages: (1) choosing a suitable switching sur-face for the desired sliding motion; and (2) designingthe sliding mode controller that brings any orbit inphase space to the switching surface and then achiev-ing the anti-synchronization of the chaotic systemseven in the presence of parameter and disturbanceuncertainties. This is precisely why this method ofanti-synchronization is considered to be robust underuncertainties and external disturbances. The slidingsurface can be defined as follows:

𝑠(𝑒) = 𝐶𝑒, (4)

where 𝐶 = [𝑐1, 𝑐2, 𝑐3] is a constant vector. Choose thecontroller 𝑢(𝑡) as

𝑢(𝑡) = −𝑓(𝑥)− 𝑔(𝑦)− 𝐹 (𝑥)��−𝐺(𝑦)𝛽 −𝐾[ 𝑠

|𝑠|+ 𝛾

],

(5)where 𝐾 = [𝑘1, 𝑘2, 𝑘3]

𝑇 is a constant gain vector thatsatisfies 𝐶𝐾 > 0 and 𝑠 = 𝑠(𝑒) is a switching surfacewhich prescribes the desired dynamics. Here �� and 𝛽are the parameter estimates of 𝛼 and 𝛽, respectively;and 𝛾 is a positive real number. The resultant errordynamics is then

�� = 𝐹 (𝑥)(𝛼− ��) +𝐺(𝑦)(𝛽 − 𝛽)−𝐾[ 𝑠

|𝑠|+ 𝛾

].(6)

*Supported by the Malaysian Ministry of Higher Education under Grant No UKM–DLP–2011–016.**Corresponding author. Email: [email protected]© 2012 Chinese Physical Society and IOP Publishing Ltd

120505-1

CHIN.PHYS. LETT. Vol. 29, No. 12 (2012) 120505

The parameters update laws can be chosen as

˙𝛼 = 𝐹 (𝑥)𝑇𝜆, ��(0) = ��0,˙𝛽 = 𝐺(𝑦)𝑇𝜆, 𝛽(0) = 𝛽0,

(7)

where 𝜆 = 𝑠[𝑐1, 𝑐2, 𝑐3]𝑇 = 𝑠𝐶𝑇 ; ��0 and 𝛽0 are the ini-

tial values of the update parameters �� and 𝛽, respec-tively. To check the stability of the proposed methodthe following theorem contains the necessary condi-tions for the stability of error system in Eq. (6).

(a)

(b)

(c)

x1x2

30

20

10

0

-10

-20

y1y2

40

30

20

10

0

-10

-20

-30

z1z2

t

1086420

60

50

40

30

20

10

0

Fig. 1. State trajectories of drive system (12) and re-sponse system (13) without controls (𝑢𝑖 = 0, 𝑖 = 1, 2, 3)under the initial condition (𝑥1(0), 𝑦1(0), 𝑧1(0)) = (𝑥2(0),𝑦2(0), 𝑧2(0)): (a) signals 𝑥1 and 𝑥2, (b) signals 𝑦1 and 𝑦2,(c) signals 𝑧1 and 𝑧2.

Theorem 1: Considering that adaptive slidingmode control input law in Eq. (5) is used to controlerror system in Eq. (6) with update laws of parame-ters in Eq. (7), then error system in Eq. (6) is asymp-totically and globally stable.

Proof: To check the stability of the controlled sys-tem, one can consider the following Lyapunov candi-date function:

𝑉 =1

2𝑠2 +

1

2‖𝛼− ��‖2 + 1

2‖𝛽 − 𝛽‖2. (8)

The time derivative of Eq. (8) is

�� = ��𝑠− (𝛼− ��)𝑇 ˙𝛼− (𝛽 − 𝛽)𝑇˙𝛽

= 𝑠𝐶��− (𝛼− ��)𝑇 ˙𝛼− (𝛽 − 𝛽)𝑇˙𝛽

= 𝑠��𝑇𝐶𝑇 − (𝛼− ��)𝑇 ˙𝛼− (𝛽 − 𝛽)𝑇˙𝛽. (9)

Introducing update laws in Eq. (7) into the right-handside of Eq. (9), one obtains

�� =[(𝛼− ��)𝑇𝐹 (𝑥)𝑇 + (𝛽 − 𝛽)𝑇𝐺(𝑦)𝑇

−𝐾𝑇[ 𝑠

|𝑠|+ 𝛾

]]𝑠𝐶𝑇 − (𝛼− ��)𝑇𝐹 (𝑥)𝑇𝜆

− (𝛽 − 𝛽)𝑇𝐺(𝑦)𝑇𝜆

=(𝛼− ��)𝑇𝐹 (𝑥)𝑇𝜆+ (𝛽 − 𝛽)𝑇𝐺(𝑦)𝑇𝜆

−𝐾𝑇𝐶𝑇[ 𝑠2

|𝑠|+ 𝛾

]− (𝛼− ��)𝑇𝐹 (𝑥)𝑇𝜆

− (𝛽 − 𝛽)𝑇𝐺(𝑦)𝑇𝜆. (10)

Then Eq. (10) reduces to

�� = −𝐶𝐾[ 𝑠2

|𝑠|+ 𝛾

]. (11)

Since both 𝑠2 > 0 and |𝑠| > 0 when 𝑒 = 0 and 𝐶𝐾 > 0,the inequality �� < 0 holds.

(a) (b)

(c)

(e)

(d)

(f)

30

20

10

0

-10

-20

-30

30

20

10

0

-10

-20

-3060

40

20

0

-20

-40

-60

40

30

20

10

0

-10

t

1086420

60

50

40

30

20

10

0

-10

t

1086420

50

40

30

20

10

0

-10

x1x2

a1b1c1

a2b2c2

e1e2e3

z1z2

y1y2

Fig. 2. State trajectories of drive system (12) and re-sponse system (13): (a) signals 𝑥1 and 𝑥2, (b) signals 𝑦1and 𝑦2, (c) signals 𝑧1 and 𝑧2, (d) the error signals 𝑒1, 𝑒2and 𝑒3 between the chaotic Lorenz system and the chaoticChen system under the controller (15); (f) the parameterestimates of the Lorenz system, (e) the parameter esti-mates of the Chen system

Since 𝑉 is positive definite and �� is negative semi-definite, then the error system is stable in the sense ofLyapunov and the slave system (2) anti-synchronizesthe master systems (1) asymptotically and globally.In order to observe anti-synchronization behavior be-tween two different chaotic systems via adaptive slid-ing mode control, the Lorenz system[13] is assumed asthe drive system and the Chen system[14] is taken asthe response system. The drive system can be writtenas

𝑥1 = 𝑎1(𝑦1 − 𝑥1), 𝑦1 = 𝑏1𝑥1 − 𝑥1𝑧1 − 𝑦1,

𝑧1 =𝑥1𝑦1 − 𝑐1𝑧1, (12)

and the response system can be written as

𝑥2 = 𝑎2(𝑦2 − 𝑥2) + 𝑢1,

𝑦2 =(𝑏2 − 𝑎2)𝑥2 − 𝑥2𝑧2 + 𝑏2𝑦2 + 𝑢2,

𝑧2 =𝑥2𝑦2 − 𝑐2𝑧2 + 𝑢3. (13)

120505-2

CHIN.PHYS. LETT. Vol. 29, No. 12 (2012) 120505

Our goal is to find proper control functions 𝑢𝑖(𝑖 =1, 2, 3) and parameter update rule, such that system(13) anti-synchronizes system (12) asymptotically, i.e.,lim𝑡→∞

‖𝑒‖ = 0, where 𝑒 = [𝑒1, 𝑒2, 𝑒3]𝑇 . If the two

systems are without controls (𝑢𝑖 = 0, 𝑖 = 1, 2, 3)and the initial condition is (𝑥1(0), 𝑦1(0), 𝑧1(0)) =(𝑥2(0), 𝑦2(0), 𝑧2(0)), then the trajectories of the twosystems will quickly separate each other and becomeirrelevant (see Figs. 1(a)–1(c)). However, when con-trols are applied, the two systems will approach anti-synchronization for any initial conditions by appropri-ate control functions. We shall propose the followingadaptive control law for system (13) The control pa-rameters are chosen as 𝐶 = (1, 1,−1),𝐾 = (5, 10, 0)𝑇

and 𝛾 = 0.01. Then the switching surface is equal to

𝑠(𝑒) = 𝑒1 + 𝑒2 − 𝑒3, (14)

and the adaptive sliding mode control law for the sys-tem is

𝑢1 = − 𝑎1(𝑦1 − 𝑥1)− 𝑎2(𝑦2 − 𝑥2)−5𝑠

|𝑠|+ 0.01,

𝑢2 = − 𝑏1𝑥1 + 𝑥1𝑧1 + 𝑦1 − (𝑏2 − 𝑎2)𝑥2 + 𝑥2𝑧2

− 𝑏2𝑦2 −10𝑠

|𝑠|+ 0.01,

𝑢3 = − 𝑥1𝑦1 + 𝑐1𝑧1 − 𝑥2𝑦2 + 𝑐2𝑧2, (15)

where 𝑎1, 𝑏1, 𝑐1, 𝑎2, 𝑏2 and 𝑐2 are the estimates of𝑎1, 𝑏1, 𝑐1, 𝑎2, 𝑏2 and 𝑐2 respectively. We have the up-date parameters’ law as follows:

˙𝑎1 = 𝑠(𝑦1 − 𝑥1),˙𝑏1 = 𝑠𝑥1, ˙𝑐1 = 𝑠𝑧1,

˙𝑎2 = 𝑠(𝑦2 − 𝑥2)− 𝑠𝑥2,˙𝑏2 = 𝑠(𝑥2 + 𝑦2), ˙𝑐2 = 𝑠𝑧2.

(16)

To check the stability of the controlled system, one canconsider the following Lyapunov candidate function:

𝑉 =1

2𝑠2 +

1

2‖𝛼− ��‖2 + 1

2‖𝛽 − 𝛽‖2. (17)

The time derivative of Eq. (17) is

�� = ��𝑠− (𝛼− ��)𝑇 ˙𝛼− (𝛽 − 𝛽)𝑇˙𝛽

= 𝑠𝐶��− (𝑎1 − 𝑎1) ˙𝑎1 − (𝑏1 − 𝑏1)˙𝑏1 − (𝑐1 − 𝑐1) ˙𝑐1

− (𝑎2 − 𝑎2) ˙𝑎2 − (𝑏2 − 𝑏2)˙𝑏2 − (𝑐2 − 𝑐2) ˙𝑐2

=(𝑠𝑒1 + 𝑠𝑒2 − 𝑠𝑒3)− (𝑎1 − 𝑎1) ˙𝑎1 − (𝑏1 − 𝑏1)˙𝑏1

− (𝑐1 − 𝑐1) ˙𝑐1 − (𝑎2 − 𝑎2) ˙𝑎2 − (𝑏2 − 𝑏2)˙𝑏2

− (𝑐2 − 𝑐2) ˙𝑐2. (18)

Introducing the update laws (16) into the right-handside of Eq. (18), one obtains

�� = 𝑠(𝑎1 − 𝑎1)(𝑦1 − 𝑥1) + 𝑠(𝑎2 − 𝑎2)(𝑦2 − 𝑥2)

− 5𝑠2

|𝑠|+ 𝛾+ 𝑠(𝑏1 − 𝑏1)𝑥1 + 𝑠(𝑏2 − 𝑏2)𝑥2

− 𝑠(𝑎2 − 𝑎2)𝑥2 + 𝑠(𝑏2 − 𝑏2)𝑦2 −10𝑠2

|𝑠|+ 𝛾

+ 𝑠(𝑐1 − 𝑐1)𝑧1 + 𝑠(𝑐2 − 𝑐2)𝑧2

− (𝑎1 − 𝑎1)𝑠(𝑦1 − 𝑥1)

− (𝑏1 − 𝑏1)𝑠𝑥1 − (𝑐1 − 𝑐1)𝑠𝑧1

− (𝑎2 − 𝑎2)𝑠(𝑦2 − 𝑥2) + (𝑎2 − 𝑎2)𝑠𝑥2

− (𝑏2 − 𝑏2)𝑠(𝑥2 + 𝑦2)− (𝑐2 − 𝑐2)𝑠𝑧2. (19)

Then Eq. (19) reduces to

�� = − 15𝑠2

|𝑠|+ 𝛾. (20)

Since 𝑉 is positive definite, and �� is negativesemi-definite. Then the error system is stable inthe sense of Lyapunov and the response system(13) anti-synchronizes the drive system (12) asymp-totically and globally. In the numerical simula-tions, the fourth-order Runge–Kutta method is usedto solve the systems with time step size 0.001.For this numerical simulation, we assume the ini-tial conditions (𝑥1(0), 𝑦1(0), 𝑧1(0)) = (6, 3, 7) and(𝑥2(0), 𝑦2(0), 𝑧2(0)) = (2, 7, 4). Hence the error sys-tem has the initial values 𝑒1(0) = 8, 𝑒2(0) = 10and 𝑒3(0) = 11. The systems’ parameters are cho-sen as 𝑎1 = 10, 𝑏1 = 28, 𝑐1 = 8/3 and 𝑎2 = 35,𝑏2 = 28, 𝑐2 = 3 in the simulations such that both sys-tems exhibit chaotic behavior. The initial values forthe estimated parameters are chosen as 𝑎1(0) = 10,𝑏1(0) = 10, 𝑐1(0) = 10, 𝑎2(0) = 10, 𝑏2(0) = 10 and𝑐2(0) = 10. Anti-synchronization of the systems (13)and (12) via adaptive sliding mode control law (15) areshown in Fig. 2. Figures 2(a)–2(c) display the statetrajectories of drive system (12) and response system(13). Figure 2(d) displays the error signals 𝑒1, 𝑒2, 𝑒3 ofthe Lorenz and the Chen systems under the controller(15). Figures 2(e) and 2(f) shows the parameter esti-mates of the Lorenz and Chen systems, respectively.

References[1] Yang T and Chua L Chua 1996 IEEE Trans. Circuits Syst.

I 43 817[2] Liao T L and Tsai S H 2000 Chaos Solitons Fractals 11

1387[3] Feki M 2003 Chaos Solitons Fractals 18 141[4] El-Dessoky M 2009 Chaos Solitons Fractals 4 1797[5] Al-Sawalha M M and Noorani M S M 2008 Chin. Phys.

Lett. 25 2743[6] Al-Sawalha M M and Noorani M S M 2008 Open Syst. Inf.

Dyn. 4 371[7] Al-Sawalha M M and Noorani M S M 2009 Chaos Solitons

Fractals 42 179[8] Al-Sawalha M M and Noorani M S M 2010 Commun. Non-

linear Sci. Numer. Simul. 15 1047[9] Al-Sawalha M M and Noorani M S M 2009 Phys. Lett. A

32 2857[10] Al-Sawalha M M and Noorani M S M 2010 Comput. Math.

Appl. 10 3234[11] Zribi M, Smaoui N and Salim H 2009 Chaos Solitons Frac-

tals 5 3197[12] Zhao Y and Wang W 2009 Chaos Solitons Fractals 41 60[13] Lorenz E N 1963 J. Atmos. Sci. 2 130[14] Chen G and Ueta T 1999 Int. J. Bifur. Chaos 7 1465

120505-3

Chinese Physics LettersVolume 29 Number 12 December 2012

GENERAL

120201 Application of the Binary Bell Polynomials Method to the Dissipative (2+1)-DimensionalAKNS EquationLIU Na, LIU Xi-Qiang

120202 Wave Interaction and Resonance in a Non-Ideal GasRajan Arora, Mohd. Junaid Siddiqui, V. P. Singh

120301 Quantum Fidelity and Thermal Phase Transitions in a Two-Dimensional Spin SystemWANG Bo, HUANG Hai-Lin, SUN Zhao-Yu, KOU Su-Peng

120302 Violation of Leggett–Garg Inequalities in Single Quantum DotsSUN Yong-Nan, ZOU Yang, GE Rong-Chun, TANG Jian-Shun, LI Chuan-Feng

120303 Quantum Stackelberg Duopoly with Continuous Distributed Incomplete InformationWANG Xia, HU Cheng-Zheng

120501 Propagation of Spiking and Burst-Spiking Synchronous States in a Feed-Forward NeuronalNetworkZHANG Xi, HUANG Hong-Bin, LI Pei-Jun, WU Fang-Ping, WU Wang-Jie, JIANG Min

120502 Generalized Zero-Temperature Glauber Dynamics in a Two-Dimensional Square LatticeMENG Qing-Kuan, FENG Dong-Tai, GAO Xu-Tuan, MEI Yu-Xue

120503 Nonlocal Symmetry of the Lax Equation Related to Riccati-Type PseudopotentialWANG Yun-Hu, CHEN Yong, XIN Xiang-Peng

120504 Quantum FrictionRoumen Tsekov

120505 Anti-Synchronization of Chaotic Systems via Adaptive Sliding Mode ControlWafaa Jawaada, M. S. M. Noorani, M. Mossa Al-sawalha

120701 Acoustic Nonlinearity of a Laser-Generated Surface Wave in a Plastically DeformedAluminum AlloyKIM Chung-Seok, JHANG Kyung-Young

120702 High Performance Micro CO Sensors Based on ZnO-SnO2 Composite Nanofibers withAnti-Humidity CharacteristicsYUE Xue-Jun, HONG Tian-Sheng, XIANG Wei, CAI Kun, XU Xing

THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS121101 An Anomaly Associated with Ward–Takahashi Identity for Pseudo-Tensor Current in QED

BAO Ai-Dong, SUN Yi-Qian, WANG Dan

NUCLEAR PHYSICS122101 Photon Linear Polarization Coefficient of the Radiative Capture Process 2H(p, γ)3He at

Thermal EnergiesH. Sadeghi

122102 Effect of Short-Range and Tensor Force Correlations on High-Density Behavior of SymmetryEnergyXU Chang, REN Zhong-Zhou

122301 The Neutrino Energy Loss by Electron Capture of Nuclides 52,53,54,55,56Fe in Core-CollapseSupernovaLIU Jing-Jing

ATOMIC AND MOLECULAR PHYSICS

123101 Stereodynamics Study of Li+HF/DF/TF→LiF+H/D/T Reactions on X2A′ PotentialEnergy SurfaceTAN Rui-Shan, LIU Xin-Guo, HU Mei

123201 Experimental Determination (∼mHz) of the Ground-State Hyperfine Separation of Trapped199Hg+ in a Hyperbolic Paul TrapHE Yue-Hong, SHE Lei, CHEN Yi-He, YANG Yu-Na, LIU Hao, LI Jiao-Mei

FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDINGAPPLICATIONS)

124201 The 1 × 4 Optical Splitters Based on Silicon Photonic Crystal Self-Collimation RingResonatorsZHUANG Dong-Xia, CHEN Xi-Yao, LI Jun-Jun, QIANG Ze-Xuan, JIANG Jun-Zhen, CHEN Zhi-Yong,QIU Yi-Shen, LI Hui

124202 Ultrastable Fiber-Based Time-Domain Balanced Homodyne Detector for QuantumCommunicationWANG Xu-Yang, BAI Zeng-Liang, DU Peng-Yan, LI Yong-Min, PENG Kun-Chi

124203 Information Transferring between a Photon’s Orbital Angular Momentum and FrequencyLIU Rui-Feng, ZHANG Pei, GAO Hong, LI Fu-Li

124204 A Switchable Multi-wavelength Erbium-Doped Photonic Crystal Fiber Laser with LinearCavity ConfigurationZHENG Wan-Jun, CHENG Jian-Qun, RUAN Shuang-Chen, ZHANG Min, LIU Wen-Li, YANG Xi,ZHANG Ying-Ying

124205 Terahertz Wave Confinement in Pillar Photonic Crystal with a Tapered Waveguide and aPoint DefectWANG Chang-Hui, KUANG Deng-Feng, CHANG Sheng-Jiang, LIN Lie

124206 A Switchable and Tunable Dual-Wavelength Actively Mode-Locked Fiber Laser Based onDispersion TuningMEI Jia-Wei, XIAO Xiao-Sheng, GUI Li-Li, XU Ming-Rui, YANG Chang-Xi

124207 Three-Dimensional Hermite–Bessel–Gaussian Soliton Clusters in Strongly Nonlocal MediaJIN Hai-Qin, LIANG Jian-Chu, CAI Ze-Bin, LIU Fei, YI Lin

124208 Analytic Solutions for the Spectral Responses of RCA-Grating-Based Waveguide DevicesZENG Xiang-Kai, WEI Lai

124209 The Generation Mechanism of Airy–Bessel Wave Packets in Free SpaceREN Zhi-Jun, YING Chao-Fu, FAN Chang-Jiang, WU Qiong

124210 Blue-Extended Supercontinuum Generation in Photonic Crystal Fibers with PicosecondPulse PumpingZHU Xian, ZHANG Xin-Ben, CHEN Xiang, PENG Jing-Gang, DAI Neng-Li, LI Jin-Yan

124211 Temporal, Spectral and Spatial Characterization of High-Energy Laser Pulse with SmallBandwidth Propagating through Long PathDENG Xue-Wei, WANG Fang, JIA Huai-Ting, XIANG Yong, FENG Bin, LI Ke-Yu, ZHOU Li-Dan

124212 Adaptive Polarization Control of Fiber Amplifier Based on SPGD AlgorithmXIONG Yu-Peng, SU Rong-Tao, LI Xiao, HOU Pu, WANG Xiao-Lin, XU Xiao-Jun

124301 Analysis of Imperfect Acoustic Cloaking ResonancesKIM Seungil

124302 Monte Carlo Simulation of Scattered Light with Shear Waves Generated by AcousticRadiation Force for Acousto-Optic ImagingLU Ming-Zhu, WU Yu-Peng, SHI Yu, GUAN Yu-Bo, GUO Xiao-Li, WAN Ming-Xi

124701 Mixed Convection Heat Transfer in Micropolar Nanofluid over a Vertical Slender CylinderAbdul Rehman, S. Nadeem

124702 The Normalized Analysis of a Surface Heterogeneous Reaction of a Propane/Air Mixtureinto a Micro-ChannelA. Fanaee, J. A. Esfahani

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES125201 Temperature Characteristics of Cathode Sheath in High-Pressure Volume Discharge Derived

from Emanating Shock WaveYANG Chen-Guang, XU Yong-Yue, ZUO Du-Luo

CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMALPROPERTIES

126101 Determination of the Lattice Parameters of a Si Nanobelt in a Tensile Test Process Using anMEMS ActuatorZENG Hong-Jiang, LI Tie, JIN Qin-Hua, XU Fang-Fang, WANG Yue-Lin

126102 Growth of Self-Catalyzed InP Nanowires by Metalorganic Chemical Vapour DepositionLV Xiao-Long, ZHANG Xia, YAN Xin, LIU Xiao-Long, CUI Jian-Gong, LI Jun-Shuai,HUANG Yong-Qing, REN Xiao-Min

126103 A Raman Study of the Origin of Oxygen Defects in Hexagonal Manganite Thin FilmsCHEN Xiang-Bai, HIEN Nguyen Thi Minh, YANG In-Sang, LEE Daesu, NOH Tae-Won

126801 A Potential Hydrogen-Storage Media: C2H4 and C5H5 Molecules Doped with Rare EarthAtomsLEI Hong-Wen, ZHANG Hong, GONG Min, WU Wei-Dong

126802 Modification of Optical BandGap and SurfaceMorphology of NiTsPc Thin FilmsMuhamad Saipul Fakir, Zubair Ahmad Khaulah Sulaiman

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL,MAGNETIC, AND OPTICAL PROPERTIES

127101 New Method to Deal with Three-Dimensional Electron Gas with a Strong Correlation EffectYU Zhi-Ming, GUO Qian, LIU Yu-Liang

127102 Influence of Oxygen Partial Pressure on the Fermi Level of ZnO Films Investigated byKelvin Probe Force MicroscopySU Ting, ZHANG Hai-Feng

127103 Influence of Pressure on the Structural, Electronic and Mechanical Properties of CubicSrHfO3: A First-Principles StudyFENG Li-Ping, WANG Zhi-Qiang, LIU Qi-Jun, TAN Ting-Ting, LIU Zheng-Tang

127104 A New Method to Calculate the Rashba Spin Splitting in III-Nitride HeterostructuresLI Ming, SUN Gang, FAN Li-Bo

127201 Onset for the Electron Velocity Overshoot in Indium NitrideCloves G. Rodrigues

127301 Analysis of Off-State Leakage Current Characteristics and Mechanisms of NanoscaleMOSFETs with a High-k Gate DielectricLIU Hong-Xia, MA Fei

127302 Laser-Induced Indium-Diffusion into Cadmium Sulfide Thin Film for Solar Cell ApplicationsKIM Nam-Hoon, MYUNG Kuk Do, LEE Woo-Sun

127303 GaSb p-Channel Metal-Oxide-Semiconductor Field-Effect Transistors with Ni/Pt/AuSource/Drain Ohmic Contacts

WU Li-Shu, SUN Bing, CHANG Hu-Dong, ZHAO Wei, XUE Bai-Qing, ZHANG Xiong, LIU Hong-Gang

127304 Ultracompact Refractive Index Sensor Based on Surface-Plasmon-Polariton InterferenceWANG Chen, CHEN Jian-Jun, TANG Wei-Hua, XIAO Jing-Hua

127305 Enhanced Photovoltaic Properties of Gradient Doping Solar CellsZHANG Chun-Lei, DU Hui-Jing, ZHU Jian-Zhuo, XU Tian-Fu, FANG Xiao-Yong

127501 Influence of Film Roughness on the Soft Magnetic Properties of Fe/Ni Multilayers

LUO Zhi-Yuan, TANG Jia, MA Bin, ZHANG Zong-Zhi, JIN Qing-Yuan, WANG Jian-Ping

127601 Preparing Pseudo-Pure States in a Quadrupolar Spin System Using Optimal ControlTAN Yi-Peng, NIE Xin-Fang, LI Jun, CHEN Hong-Wei, ZHOU Xian-Yi, PENG Xin-Hua, DU Jiang-Feng

127701 Ultrasonic Energy Transference Based on an MEMS ZnO Film ArrayWU Shao-Hua, ZHAO Zhan, ZHAO Jun-Juan, GUO Li-Jun, DU Li-Dong, FANG Zhen, KONG De-Yi,XIAO Li, GAO Zhong-Hua

127801 A Novel Efficient Red Emitting Iridium Complex for Polymer Light Emitting DiodesHU Zheng-Yong, YANG Jian-Kui, LUO Jing, LIANG Min, WANG Jing

127802 An Improvement on the Junction Temperature Measurement of Light-Emitting Diodes byusing the Peak Shift Method Compared with the Forward Voltage MethodHE Su-Ming, LUO Xiang-Dong, ZHANG Bo, FU Lei, CHENG Li-Wen, WANG Jin-Bin, LU Wei

127803 The Evolution of Defects in Deformed Cu-Ni-Si Alloys during Isochronal Annealing Studiedby Positron AnnihilationQI Ning, JIA Yan-Lin, LIU Hui-Qun, YI Dan-Qing, CHEN Zhi-Quan

127804 Origin of Ferromagnetism in Zn1−xCoxO Thin Films: Evidences Provided by Hard and SoftX-Ray Absorption SpectroscopyXI Shi-Bo, CUI Ming-Qi, QIN Xiu-Fang, XU Xiao-Hong, XU Wei, ZHENG Lei, ZHOU Jing, LIU Li-Juan,YANG Dong-Liang, GUO Zhi-Ying

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE ANDTECHNOLOGY

128101 The High Nitrogen Pressure Synthesis of Manganese NitrideSI Ping-Zhan, JIANG Wei, WANG Hai-Xia, ZHONG Min, GE Hong-Liang, CHOI Chul-Jin,LEE Jung-Goo

128102 The Synthesis and Characterization of Peach-Like ZnOA. Kamalianfar, S. A. Halim, Siamak Pilban Jahromi, M. Navasery, Fasih Ud Din, K. P. Lim, S. K. Chen,J. A. M. Zahedi

128103 The Effects of Heating Mechanism on Granular Gases with a Gaussian Size DistributionLI Rui, XIAO Ming, LI Zhi-Hao, ZHANG Duan-Ming

128401 Independently Tunable Multichannel Filters Based on Graphene Superlattices with FractalPotential PatternsZHANG Hui-Yun, ZHANG Yu-Ping, GAO Ying, YIN Yi-Heng

128501 The Structural and Electrical Properties of Al/Pb(Zr0.52Ti0.48)O3/Al2O3/Si with an Al2O3

Layer Prepared by using the Molecular Atomic Deposition MethodYANG Yi, ZHOU Chang-Jian, PENG Ping-Gang, XIE Dan, REN Tian-Ling, PAN Xiao, LIU Jing-Song

128502 A 50–60V Class Ultralow Specific on-Resistance Trench Power MOSFETHU Sheng-Dong, ZHANG Ling, CHEN Wen-Suo, LUO Jun, TAN Kai-Zhou, GAN Ping, ZHU Zhi,WU Xing-He

128901 Topological and Spectral Perturbations in Complex NetworksYAN Xin, WU Yang

128902 Pheromone Static Routing Strategy for Complex NetworksHU Mao-Bin, Henry Y.K. Lau, LING Xiang, JIANG Rui

128903 Self-Similarity in Game-Locked AggregationWANG Chao, XIONG Wan-Ting, WANG You-Gui