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 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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