Synchronization of non-chaotic dynamical systems

TL;DR

This paper investigates how non-chaotic systems with stable chaos synchronize when driven by annealed noise, revealing a phase transition in the directed percolation class and linking synchronization thresholds to perturbation propagation.

Contribution

It demonstrates that synchronization in stable chaos systems follows a directed percolation universality class and connects the coupling threshold to perturbation velocity.

Findings

Synchronization transition belongs to directed percolation class

Coupling threshold relates to perturbation propagation velocity

Supports equivalence between stable chaos models and cellular automata

Abstract

A synchronization mechanism driven by annealed noise is studied for two replicas of a coupled-map lattice which exhibits stable chaos (SC), i.e. irregular behavior despite a negative Lyapunov spectrum. We show that the observed synchronization transition, on changing the strength of the stochastic coupling between replicas, belongs to the directed percolation universality class. This result is consistent with the behavior of chaotic deterministic cellular automata (DCA), supporting the equivalence Ansatz between SC models and DCA. The coupling threshold above which the two system replicas synchronize is strictly related to the propagation velocity of perturbations in the system.