Synchronization of coupled chaotic maps

TL;DR

This paper establishes a sufficient condition for synchronization in coupled one-dimensional maps, linking spectral graph properties to synchronization, and demonstrates the benefits of random connectivity through theoretical analysis and numerical experiments.

Contribution

It introduces a new spectral condition for synchronization and relates graph eigenvalues to synchronization likelihood in coupled chaotic systems.

Findings

Graphs with eigenvalues near 1 facilitate synchronization.

Random connectivity enhances synchronization in chaotic networks.

Spectral properties of specific graphs influence synchronization behavior.

Abstract

We prove a sufficient condition for synchronization for coupled one-dimensional maps and estimate the size of the window of parameters where synchronization takes place. It is shown that coupled systems on graphs with positive eigenvalues (EVs) of the normalized graph Laplacian concentrated around 1 are more amenable for synchronization. In the light of this condition, we review spectral properties of Cayley, quasirandom, power-law graphs, and expanders and relate them to synchronization of the corresponding networks. The analysis of synchronization on these graphs is illustrated with numerical experiments. The results of this paper highlight the advantages of random connectivity for synchronization of coupled chaotic dynamical systems.