Emergence of chaotic cluster synchronization in heterogeneous networks

Rodrigo M Corder; Zheng Bian; Tiago Pereira; Antonio Montalbán

doi:10.1063/5.0169628

Emergence of chaotic cluster synchronization in heterogeneous networks

Chaos. 2023 Sep 1;33(9):091103. doi: 10.1063/5.0169628.

Authors

Rodrigo M Corder¹, Zheng Bian², Tiago Pereira^{2

3}, Antonio Montalbán⁴

Affiliations

¹ Division of Epidemiology and Biostatistics, School of Public Health, University of California, Berkeley, Berkeley, California 94720, USA.
² Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos 13566-590, Brazil.
³ Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom.
⁴ Department of Mathematics, University of California, Berkeley, Berkeley, California 94720, USA.

PMID: 37703473
DOI: 10.1063/5.0169628

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 a 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 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.