Noise, Synchrony and Correlations at the Edge of Chaos

TL;DR

This paper investigates how weak noise influences synchronization and intermittency in coupled logistic maps at the edge of chaos, revealing fat-tailed distributions and parallels with financial data.

Contribution

It demonstrates the impact of weak additive noise on intermittency and fat-tailed distributions in a coupled map system, linking nonlinear dynamics to nonextensive statistical mechanics.

Findings

Weak noise induces intermittency in coupled logistic maps.

Fat-tailed distributions emerge, well-described by $q$-Gaussians.

Interoccurrence times of extreme events resemble financial data patterns.

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.