Impact of bistability in the synchronization of chaotic maps with delayed coupling

TL;DR

This paper studies how bistability affects synchronization in networks of chaotic maps with delayed coupling, showing that a single attractor promotes synchronization while multiple attractors hinder it.

Contribution

It demonstrates that the presence of a single finite attractor in local dynamics is crucial for synchronization in delayed coupled chaotic maps, a novel insight into network dynamics.

Findings

Synchronization occurs with a single attractor.

Multiple chaotic attractors prevent synchronization.

Robustness across different network topologies.

Abstract

We investigate the impact of bistability in the emergence of synchronization in networks of chaotic maps with delayed coupling. The existence of a single finite attractor of the uncoupled map is found to be responsible for the emergence of synchronization. No synchronization is observed when the local dynamics has two competing chaotic attractors whose orbits are dense on the same interval. This result is robust for regular networks with variable ranges of interaction and for more complex topologies.