1 Negative Differential Resistance of Extended Viologen. Oscillations with Odd Harmonic Frequencies. Stochastic Resonance. J. Heyrovský Institute of Physical Chemistry, AS CR, Prague Institute of Organic Chemistry & Biochemistry, AS CR, Prague Lubomír Pospíšil, Magdaléna Hromadová
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Negative Differential Resistance of Extended Viologen. … · 2014-07-10 · 1 Negative Differential Resistance of Extended Viologen. Oscillations with Odd Harmonic Frequencies. Stochastic
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M. Hromadová, M. Valášek, N. Fanelli, H. N. Randriamahazaka, L. PospíšilStochastic Resonance in Electron Transfer Oscillations of Extended Viologen.J. Phys. Chem. C, 2014, dx.doi.org/10.1021/jp501608b
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Co-authors:
Magdaléna HROMADOVÁMichal VALÁŠEKNicolangelo FANELLIHyacinthe N. Randriamahazaka
Acknowledgement:
Grant Agency Czech Rep.,
Joint project C.N.R.-AS CR
Joint project C.N.R.S.-AS CR
24Thank you for your attention
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Chaos is lifePeriodicity is boring
Stability is death
Thank you for your attention
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Can we predict a change:
stability – periodicity – deterministic chaos
???
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Deterministic chaos random fluctuations
Observation at time tn depends on values at tn-1, tn-2, …
Functional dependence exists - may not be known
Random events do not correlate with previous eventsNo functional law
The proof of a hidden functionaldependence:
Do the observation in timeform an attractor ?
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Attractor
An attractor can be a point, a finite set ofpoints, a curve, a surface,
or even a complicated set with a fractalstructure known as a strange attractor.
Observed time series: i(t1), i(t2),…i(tn-1), i(tn)
Plotting i(t) vs i(t - 2) vs i(t - 4 )
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Extended viologen:Time delay analysis of experimental series
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Deterministic chaos random fluctuations
Diagnostic criteria
5 10
-0.5
0.0
0.5
i/A
t / s
Current-time series → Time-delayed plot →→ Phase space diagram → Attractor orbit →→ Exponential evolution → Ljapunov exponent λ
0 10 20 30 40 50
-8
-6
-4
-2
S(
n)
n
exponential divergence of nearbytrajectories for three embedded
space dimensions → λ=0.41 > 0 !!!Reconstructed attractor
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Ljapunov exponent :quantifies the stregth of chaos