Noise, synchrony, and correlations at the edge of chaos

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 probability distribution functions (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. The interoccurrence times of these extreme events are also studied in detail. Similarities with the recent analysis of financial data are also discussed.