Exponentially long transient time to synchronization of coupled chaotic circle maps in dense random networks

TL;DR

This paper investigates how large, dense networks of coupled chaotic circle maps take an exponentially long time to synchronize, especially in finite networks with less than full connectivity, revealing the nature of chaotic transients.

Contribution

It provides an exact mean-field solution for infinite networks and analyzes the scaling of transient times in finite, partially connected dense networks.

Findings

Chaotic transients have exponentially distributed escape times.

Mean time to synchronization scales exponentially with network parameters.

Incoherent states are meta-stable for certain coupling strengths.

Abstract

We study the transition to synchronization in large, dense networks of chaotic circle maps, where an exact solution of the mean-field dynamics in the infinite network and all-to-all coupling limit is known. In dense networks of finite size and link probability of smaller than one, the incoherent state is meta-stable for coupling strengths that are larger than the mean-field critical coupling. We observe chaotic transients with exponentially distributed escape times and study the scaling behavior of the mean time to synchronization.