Patterns of Chaos Synchronization

TL;DR

This paper investigates how small networks of chaotic units with time-delayed coupling can synchronize in various patterns, including complete, sublattice, and symmetry-breaking, revealing stable attractors and diverse synchronization behaviors.

Contribution

It introduces new insights into synchronization patterns in chaotic networks with time delays, including sublattice and symmetry-breaking synchronization modes.

Findings

Networks can synchronize isochronally despite delays

Multiple stable synchronization patterns exist, including sublattice and symmetry-breaking

Different network topologies exhibit distinct synchronization behaviors

Abstract

Small networks of chaotic units which are coupled by their time-delayed variables, are investigated. In spite of the time delay, the units can synchronize isochronally, i.e. without time shift. Moreover, networks can not only synchronize completely, but can also split into different synchronized sublattices. These synchronization patterns are stable attractors of the network dynamics. Different networks with their associated behaviors and synchronization patterns are presented. In particular, we investigate sublattice synchronization, symmetry breaking, spreading chaotic motifs, synchronization by restoring symmetry and cooperative pairwise synchronization of a bipartite tree.