First-order Synchronization Transition in Locally Coupled Maps

TL;DR

This paper investigates phase transitions in coupled chaotic maps on lattices, revealing a first-order transition to synchronization and a subsequent de-synchronization, with the nature of the transition depending on the map's linearity.

Contribution

It introduces a model of locally coupled maps with an effective delay and characterizes the nature of synchronization transitions, highlighting differences between linear and nonlinear maps.

Findings

First-order transition from multi-stable to synchronized phase

De-synchronization leads to two ergodic regions

Transition type depends on map differentiability

Abstract

We study a family of diffusively coupled chaotic maps on periodic d-dimensional square lattices. Even and odd sub-lattices are updated alternately, introducing an effective delay. As the coupling strength is increased, the system undergoes a first order phase transition from a multi-stable to a synchronized phase. Further increase in coupling strength shows de-synchronization where the phase space splits into two ergodic regions. We argue that the de-synchronization transition is discontinuous for piece-wise linear maps, and is continuous for non-linear maps which are differentiable.