Noise, Synchrony and Correlations at the Edge of Chaos

Abstract

We study the effect of a weak random additive noise in a linear chain of N locally-coupled logistic maps at the edge of chaos. Maps tend to synchronize for a strong enough coupling, but if a weak noise is added, very intermittent fluctuations in the returns time series are observed. This intermittency tends to disappear when noise is increased. Considering the pdfs of the returns, we observe the emergence of fat tails which can be satisfactorily reproduced by $q$-Gaussians curves typical of nonextensive statistical mechanics. Interoccurrence times of these extreme events are also studied in detail. Similarities with recent analysis of financial data are also discussed.

6 pages, 8 figures, new figure added - Version accepted for publication in Physical Review E

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• Noise induced unanimity and disorder in opinion formation
• Nonextensive Nuclear Liquid-Gas Phase Transition
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• On patterns and dynamics of Rule 22 cellular automaton