Synchronization of coupled chaotic oscillators as a phase transition

Abstract

We characterize the synchronization of an array of coupled chaotic elements as a phase transition where order parameters related to the joint probability at two sites obey power laws versus the mutual coupling strength; the phase transition corresponds to a change in the exponent of the power law. Since these studies are motivated by the behaviour of the cortical neurons in cognitive tasks, we account for the short time available to any brain decision by studying how the mutual coupling affects the transient behaviour of a synchronization transition over a fixed time interval. We present a novel feature, namely, the absence of decay of the initial defect density for small coupling.