Synchronizability determined by coupling strengths and topology on Complex Networks

TL;DR

This paper explores how coupling strengths and network topology influence synchronization in complex networks, revealing that local synchronization patterns depend on network heterogeneity and modular structure, with new parameters aiding characterization.

Contribution

It extends previous work by analyzing networks with varying degrees of heterogeneity and introduces new parameters for better characterization of synchronization phenomena.

Findings

Local synchronization patterns differ between homogeneous and heterogeneous networks.

Synchronization begins internally within modules before spreading outward as coupling increases.

New parameters effectively characterize different synchronization regimes.

Abstract

We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we unveiled how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks. Here, we provide more evidence on this phenomenon extending the previous work to networks that interpolate between homogeneous and heterogeneous topologies. We also present new details on the path towards synchronization for the evolution of clustering in the synchronized patterns. Finally, we investigate the synchronization of networks with modular structure and conclude that, in these cases, local synchronization is first attained at the most internal level of organization of modules, progressively evolving to the outer levels as the coupling constant is increased. The present work introduces new parameters that are proved to be useful for the characterization of synchronization phenomena in complex networks.