# Synchronization of spatio-temporal chaos as an absorbing phase transition: a study in 2+1 dimensions

## TL;DR

This study investigates the phase transition to synchronization in coupled 2+1 dimensional chaotic systems, identifying universality classes and effects of small differences, with implications for experimental research.

## Contribution

It extends the understanding of synchronization transitions to 2+1 dimensions and distinguishes universality classes based on damage spreading characteristics.

## Key findings

- Transition belongs to MN or DP universality classes depending on damage spreading.
- Numerical estimates for MN in 2+1 dimensions are provided.
- Small differences between replicas act as an external field, characterized by a critical exponent.

## Abstract

The synchronization transition between two coupled replicas of spatio-temporal chaotic systems in 2+1 dimensions is studied as a phase transition into an absorbing state - the synchronized state. Confirming the scenario drawn in 1+1 dimensional systems, the transition is found to belong to two different universality classes - Multiplicative Noise (MN) and Directed Percolation (DP) - depending on the linear or nonlinear character of damage spreading occurring in the coupled systems. By comparing coupled map lattice with two different stochastic models, accurate numerical estimates for MN in 2+1 dimensions are obtained. Finally, aiming to pave the way for future experimental studies, slightly non-identical replicas have been considered. It is shown that the presence of small differences between the dynamics of the two replicas acts as an external field in the context of absorbing phase transitions, and can be characterized in terms of a suitable critical exponent.