Stretched-exponential dynamics in a chain of coupled chaotic oscillators

¹ Department of Physics and Astronomy and CMSS, Ohio University Athens, OH 45701, USA
² Département de Physique, Université de Montréal C.P. 6128, Succ. Centre-ville, Montréal (Québec), Canada H3C 3J7

Corresponding authors: hunt@helios.phy.ohiou.edu, normand.mousseau@umontreal.ca

Received: 9 April 2002
Accepted: 26 September 2002

Abstract

We measured a stretched-exponential trap time distribution, , over many decades in a one-dimensional array of coupled chaotic electronic elements just above a crisis-induced intermittency transition. This distribution is obtained by measuring the time an oscillator spends in the same state. There is strong spatial heterogeneity and individual sites display a dynamics ranging from near power law to near exponential 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.