Stretched exponential dynamics in a chain of coupled chaotic oscillators

TL;DR

This study investigates stretched exponential dynamics in a chain of coupled chaotic oscillators, revealing system-independent behavior and heterogeneity, which can be modeled with coupled-map lattices and quenched disorder.

Contribution

It demonstrates that stretched exponential behavior occurs in coupled chaotic systems and can be modeled without frozen disorder, highlighting its fundamental chaotic origin.

Findings

Global dynamics are stretched exponential despite local heterogeneity.

Model reproduces experimental heterogeneity with quenched disorder.

Local dynamics range from near power law to near exponential.

Abstract

We measure stretched exponential behavior, exp(- (t/t_0)**beta), over many decades in a one-dimensional array of coupled chaotic electronic elements just above a crisis-induced intermittency transition. There is strong spatial heterogeneity and individual sites display a dynamics ranging from near power law ($\beta=0$) to near exponential ($\beta=1$) while the global dynamics, given by a spatial average, remains stretched exponential. These results can be reproduced quantitatively with a one-dimensional coupled-map lattice and thus appear to be system independent. In this model, local stretched exponential dynamics is achieved without frozen disorder and is a fundamental property of the coupled system. The heterogeneity of the experimental system can be reproduced by introducing quenched disorder in the model. This suggests that the stretched exponential dynamics can arise as a purely chaotic phenomenon.