Optimizing synchronizability of networks

TL;DR

This paper explores how network structural properties influence the synchronization of coupled oscillators, demonstrating that certain configurations like low clustering and disassortative patterns enhance synchronizability.

Contribution

It introduces an optimization approach using Memory Tabu Search to improve network synchronizability while preserving degree distribution, revealing key structural factors.

Findings

Lower clustering improves synchronizability

Disassortative networks synchronize more easily

Heterogeneity in scale-free networks is crucial for synchronization

Abstract

In this paper, we investigate the factors that affect the synchronization of coupled oscillators on networks. By using the edge-intercrossing method, we keep the degree distribution unchanged to see other statistical properties' effects on network's synchronizability. By optimizing the eigenratio $R$ of the coupling matrix with \textit{Memory Tabu Search} (MTS), we observe that a network with lower degree of clustering, without modular structure and displaying disassortative connecting pattern may be easy to synchronize. Moreover, the optimal network contains fewer small-size loops. The optimization process on scale-free network strongly suggests that the heterogeneity plays the main role in determining the synchronizability.