Synchronization on complex networks with different sorts of communities

TL;DR

This paper studies how oscillators synchronize on complex networks with multiple community types, revealing a phenomenon called Community Grouping where same-type communities synchronize before global synchronization.

Contribution

It introduces the concept of Community Grouping in networks with different community types and analyzes the conditions for partial and global synchronization.

Findings

Community Grouping occurs when community strength weakens.

Oscillators in the same community type synchronize first.

Global synchronization emerges at lower community strength.

Abstract

In this paper, inspired by the idea that many real networks are composed by different sorts of communities, we investigate the synchronization property of oscillators on such networks. We identify the communities by the intrinsic frequencies probability density $g(\omega)$ of Kuramoto oscillators. That is to say, communities in different sorts are functional different. For a network containing two sorts of communities, when the community strength is strong, only the oscillators in the same community synchronize. With the weakening of the community strength, an interesting phenomenon, \emph{Community Grouping}, appears: although the global synchronization is not achieved, oscillators in the same sort of communities will synchronize. Global synchronization will appear with the further reducing of the community strength, and the oscillators will rotate around the average frequency.