Synchronization of Coupled Systems with Spatiotemporal Chaos

TL;DR

This paper classifies the universality classes of synchronization transitions in coupled chaotic systems, showing cellular automata align with directed percolation and real-valued systems with spatiotemporal chaos align with KPZ universality.

Contribution

It provides a theoretical framework linking synchronization transitions in coupled systems to well-known universality classes, clarifying previous conflicting claims.

Findings

Synchronization transition in cellular automata belongs to directed percolation class.

Real-valued spatiotemporal chaotic systems follow KPZ universality class.

Numerical evidence supports the classification of these transitions.

Abstract

We argue that the synchronization transition of stochastically coupled cellular automata, discovered recently by L.G. Morelli {\it et al.} (Phys. Rev. {\bf 58 E}, R8 (1998)), is generically in the directed percolation universality class. In particular, this holds numerically for the specific example studied by these authors, in contrast to their claim. For real-valued systems with spatiotemporal chaos such as coupled map lattices, we claim that the synchronization transition is generically in the universality class of the Kardar-Parisi-Zhang equation with a nonlinear growth limiting term.