Stochastic theory of synchronization transitions in extended systems

TL;DR

This paper introduces a Langevin equation model that captures the universal behaviors of synchronization transitions in extended systems, unifying various observed phenomena through theoretical and numerical analysis.

Contribution

It presents a comprehensive Langevin equation framework that describes different types of synchronization transitions, including continuous and discontinuous, in extended systems.

Findings

The model reproduces known synchronization transition features.

Identifies conditions for continuous transitions in different universality classes.

Suggests some discontinuous transitions may be transient phenomena.

Abstract

We propose a general Langevin equation describing the universal properties of synchronization transitions in extended systems. By means of theoretical arguments and numerical simulations we show that the proposed equation exhibits, depending on parameter values, either: i) a continuous transition in the bounded Kardar-Parisi-Zhang universality class, with a zero largest Lyapunov exponent at the critical point; ii) a continuous transition in the directed percolation class, with a negative Lyapunov exponent, or iii) a discontinuous transition (that is argued to be possibly just a transient effect). Cases ii) and iii) exhibit coexistence of synchronized and unsynchronized phases in a broad (fuzzy) region. This phenomenology reproduces almost all the reported features of synchronization transitions of coupled map lattices and other models, providing a unified theoretical framework for the analysis of synchronization transitions in extended systems.