Dynamics of delayed-coupled chaotic logistic maps: influence of network topology, connectivity and delay times

TL;DR

This paper investigates how network topology, connectivity, and delay times influence the synchronization of delay-coupled chaotic logistic maps, revealing that heterogeneous delays can suppress chaos regardless of network structure.

Contribution

It demonstrates that sufficiently heterogeneous delay times lead to synchronization in chaotic networks, largely independent of topology but dependent on connectivity.

Findings

Heterogeneous delays induce synchronization in chaotic maps.

Synchronization is robust across different network topologies.

Connectivity influences the effectiveness of chaos suppression.

Abstract

We review our recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network topology and the delay times that take into account the finite velocity of propagation of interactions. We assume that the elements of the network are identical ($N$ logistic maps in the regime where the individual maps, without coupling, evolve in a chaotic orbit) and that the coupling strengths are uniform throughout the network. We show that if the delay times are sufficiently heterogeneous, for adequate coupling strength the network synchronizes in a spatially homogeneous steady-state, which is unstable for the individual maps without coupling. This synchronization behavior is referred to as ``suppression of chaos by random delays'' and is in contrast with the synchronization when all the interaction delay times are homogeneous, because with homogeneous delays the network synchronizes in a state where the elements display in-phase time-periodic or chaotic oscillations. We analyze the influence of the network topology considering four different types of networks: two regular (a ring-type and a ring-type with a central node) and two random (free-scale Barabasi-Albert and small-world Newman-Watts). We find that when the delay times are sufficiently heterogeneous the synchronization behavior is largely independent of the network topology but depends on the networks connectivity, i.e., on the average number of neighbors per node.