Scalable synchronization cluster in networked chaotic oscillators

TL;DR

This paper investigates the phenomenon of scalable cluster synchronization in networks of coupled chaotic oscillators, revealing how clusters expand with increasing coupling strength and analyzing their stability and dynamics.

Contribution

It introduces the concept of scalable synchronization clusters, analyzes their emergence using eigenvector-based methods, and studies their transient dynamics and stability.

Findings

Clusters expand gradually by recruiting oscillators as coupling increases

Eigenvector features of the network coupling matrix explain cluster scalability

Oscillators within the cluster stabilize sequentially after perturbations

Abstract

Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the other oscillators remain desynchronized. Interestingly, with the increase of the coupling strength, the cluster is expanding gradually by recruiting the desynchronized oscillators one by one. This new synchronization phenomenon, which is named ``scalable synchronization cluster", is explored theoretically by the method of eigenvector-based analysis, and it is revealed that the scalability of the cluster is attributed to the unique feature of the eigenvectors of the network coupling matrix. The transient dynamics of the cluster in response to random perturbations are also studied, and it is shown that in restoring to the synchronization state, oscillators inside the cluster are stabilized in sequence, illustrating again the hierarchy of the oscillators. The findings shed new light on the collective behaviors of networked chaotic oscillators, and are helpful for the design of real-world networks where scalable synchronization clusters are concerned.