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Anomalous synchronization threshold in coupled logistic maps

C. Anteneodo·A. M. Batista·R. L. Viana
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Abstract

We consider regular lattices of coupled chaotic maps. Depending on lattice size, there may exist a window in parameter space where complete synchronization is eventually attained after a transient regime. Close outside this window, an intermittent transition to synchronization occurs. While asymptotic transversal Lyapunov exponents allow to determine the synchronization threshold, the distribution of finite-time Lyapunov exponents, in the vicinity of the critical frontier, is expected to provide relevant information on phenomena such as intermittency. In this work we scrutinize the distribution of finite-time exponents when the local dynamics is ruled by the logistic map $x \mapsto 4x(1-x)$. We obtain a theoretical estimate for the distribution of finite-time exponents, that is markedly non-Gaussian. The existence of correlations, that spoil the central limit approximation, is shown to modify the typical intermittent bursting behavior. The present scenario could apply to a wider class of systems with different local dynamics and coupling schemes.

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C. Anteneodo, A. M. Batista, R. L. Viana. 2005-04-05. Anomalous synchronization threshold in coupled logistic maps. https://doi.org/10.1016/j.physd.2006.10.001

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