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# Chaos: Zero lag synchronisation

Date post: 23-Feb-2016
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Chaos: Zero lag synchronisation. Mathijs Vermeulen & Bart van Lith. Contents. Introduction Lang-Kobayashi equations Zero lag synchronization Bernoulli map Perturbed Bernoulli map Conclusions. Introduction. - PowerPoint PPT Presentation
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Chaos: Zero lag synchronisation Mathijs Vermeulen & Bart van Lith
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• Chaos: Zero lag synchronisationMathijs Vermeulen & Bart van Lith

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• ContentsIntroductionLang-Kobayashi equationsZero lag synchronizationBernoulli mapPerturbed Bernoulli mapConclusions

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• IntroductionPaper: Zero Lag Synchronization of Chaotic Systems with Time Delayed Couplings. Englert et al.Two chaotic semi-conductor lasers are synchronized.Bernoulli map is investigated analytically.Experimental setup used in the paper.

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• Lang Kobayashi equationsSet of coupled differential equations for that describe the dynamics of a chaotic diode laser.

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• Experimental data

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• Bernoulli mapNonlinear because of the modulo.Chaotic for > 1.Solution Lyapunov exponent = 1.5

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• Zero lag synchronizationTwo signals xt and yt;Two time delayed couplings with delay time 1 and 2;1, 2
• Zero Lag synchronization

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• Perturbed Bernoulli mapSmall non-linear perturbation on Bernoulli map.Rounds the saw-tooth edges.Works very well for small .Here = 0.13, = 1.5

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• Perturbed Bernoulli map = 1.5, = -1.7

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• ConclusionsSmall perturbations in ZLS are damped if:Coupling time constants are smaller than internal time scales; the coupling time constants are prime numbers;The same mapping is used;Works for small perturbations in the Bernouilli mapping.

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