Synchronization universality classes and stability of smooth, coupled map lattices

TL;DR

This paper investigates the stability and universality classes of synchronization transitions in coupled map lattices, revealing that chaos and stable chaos correspond to different universality classes, namely multiplicative noise and directed percolation.

Contribution

It establishes a link between the nature of chaos in coupled map lattices and the universality class of their synchronization transition.

Findings

Chaotic behavior corresponds to multiplicative noise universality class.

Stable chaos corresponds to directed percolation universality class.

Different types of chaos lead to different synchronization universality classes.

Abstract

We study two problems related to spatially extended systems: the dynamical stability and the universality classes of the replica synchronization transition. We use a simple model of one dimensional coupled map lattices and show that chaotic behavior implies that the synchronization transition belongs to the multiplicative noise universality class, while stable chaos implies that the synchronization transition belongs to the directed percolation universality class.