Delays, connection topology, and synchronization of coupled chaotic maps

TL;DR

This paper investigates how network topology and time delays influence synchronization in coupled chaotic maps, revealing that delays can enhance synchronization and lead to new collective behaviors.

Contribution

It demonstrates that connection topology and delays jointly determine synchronization, showing delays can promote synchronization and induce novel collective dynamics.

Findings

Scale-free and random networks synchronize despite delays.

Delays can facilitate synchronization where undelayed systems cannot.

Delays influence the nature of synchronized dynamics.

Abstract

We consider networks of coupled maps where the connections between units involve time delays. We show that, similar to the undelayed case, the synchronization of the network depends on the connection topology, characterized by the spectrum of the graph Laplacian. Consequently, scale-free and random networks are capable of synchronizing despite the delayed flow of information, whereas regular networks with nearest-neighbor connections and their small-world variants generally exhibit poor synchronization. On the other hand, connection delays can actually be conducive to synchronization, so that it is possible for the delayed system to synchronize where the undelayed system does not. Furthermore, the delays determine the synchronized dynamics, leading to the emergence of a wide range of new collective behavior which the individual units are incapable of producing in isolation.