On the relationship between directed percolation and the synchronization transition in spatially extended systems

TL;DR

This paper explores the synchronization transition in spatially extended systems, demonstrating its relation to the directed percolation universality class through analytical and numerical methods.

Contribution

It establishes that the synchronization transition belongs to the directed percolation class in both discontinuous and continuous models, supported by analytical and numerical evidence.

Findings

Synchronization transition is in the directed percolation class.

Existence of a critical threshold separating linear and collective regimes.

Numerical validation on coupled map lattices confirms the analytical results.

Abstract

We study the nature of the synchronization transition in spatially extended systems by discussing a simple stochastic model. An analytic argument is put forward showing that, in the limit of discontinuous processes, the transition belongs to the directed percolation (DP) universality class. The analysis is complemented by a detailed investigation of the dependence of the first passage time for the amplitude of the difference field on the adopted threshold. We find the existence of a critical threshold separating the regime controlled by linear mechanisms from that controlled by collective phenomena. As a result of this analysis we conclude that the synchronization transition belongs to the DP class also in continuous models. The conclusions are supported by numerical checks on coupled map lattices too.