Emergence of chaotic cluster synchronization in heterogeneous networks

TL;DR

This paper uncovers the mechanism behind the emergence of cluster synchronization in heterogeneous networks, providing a theoretical framework to predict and analyze their stability and onset across various systems.

Contribution

It introduces a heterogeneous mean field approximation and self-consistent theory to analyze cluster synchronization in complex, asymmetric networks, advancing understanding of their dynamical behavior.

Findings

Cluster synchronization occurs in diverse heterogeneous networks.

The developed theory predicts onset and stability of clusters.

Results apply to neural, social, and other complex systems.

Abstract

Many real-world complex systems rely on cluster synchronization to function properly. A cluster of nodes exhibits synchronous behavior while others behave erratically. Predicting the emergence of these clusters and understanding the mechanism behind their structure and variation in response to parameter change is a daunting task in networks that lack symmetry. We unravel the mechanism for the emergence of cluster synchronization in heterogeneous random networks. We develop a heterogeneous mean field approximation together with a self-consistent theory to determine the onset and stability of the cluster. Our analysis shows that cluster synchronization occurs in a wide variety of heterogeneous networks, node dynamics, and coupling functions. The results could lead to a new understanding of the dynamical behavior of networks ranging from neural to social.