Synchronization and directed percolation in coupled map lattices

TL;DR

This paper investigates synchronization in coupled map lattices with one-way coupling, identifying two regimes with distinct transition behaviors, and provides analytical insights into the transition points and critical properties.

Contribution

It introduces a synchronization mechanism for coupled map lattices and analyzes the transition regimes, including analytical approximations for critical points.

Findings

Transition has a directed percolation character in strong chaos phase

Synchronization transition occurs abruptly in weak chaos phase

Analytical approximations for transition points and critical properties

Abstract

We study a synchronization mechanism, based on one-way coupling of all-or-nothing type, applied to coupled map lattices with several different local rules. By analyzing the metric and the topological distance between the two systems, we found two different regimes: a strong chaos phase in which the transition has a directed percolation character and a weak chaos phase in which the synchronization transition occurs abruptly. We are able to derive some analytical approximations for the location of the transition point and the critical properties of the system. We propose to use the characteristics of this transition as indicators of the spatial propagation of chaoticity.