Cluster synchronization in complex network of coupled chaotic circuits: an experimental study

TL;DR

This study experimentally investigates how removing shortcut links affects synchronization in a small complex network of coupled chaotic circuits, revealing phenomena like partial and cluster synchronization dependent on network symmetry.

Contribution

It demonstrates the experimental observation of cluster synchronization in chaotic circuits and links it to network topology and symmetry, advancing understanding of controllable synchronization.

Findings

Removal of shortcut links can destroy or partially disrupt synchronization.

Cluster synchronization occurs with oscillators forming synchronized groups.

Network symmetry is crucial for the formation of cluster synchronization.

Abstract

By a small-size complex network of coupled chaotic Hindmarsh-Rose circuits, we study experimentally the stability of network synchronization to the removal of shortcut links. It is shown that the removal of a single shortcut link may destroy either completely or partially the network synchronization. Interestingly, when the network is partially desynchronized, it is found that the oscillators can be organized into different groups, with oscillators within each group being highly synchronized but are not for oscillators from different groups, showing the intriguing phenomenon of cluster synchronization. The experimental results are analyzed by the method of eigenvalue analysis, which implies that the formation of cluster synchronization is crucially dependent on the network symmetries. Our study demonstrates the observability of cluster synchronization in realistic systems, and indicates the feasibility of controlling network synchronization by adjusting network topology.