Synchronization of groups of coupled oscillators with sparse connections

¹  Department of Physics and the Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Studies, Beijing Normal University - Beijing 100875, China
²  Center for Nonlinear Studies and Department of Physics, Hong Kong Baptist University - Hong Kong, China
³  Department of Physics, California Institute of Technology - Pasadena 91125, CA, USA

Corresponding author: zgzheng@bnu.edu.cn

Received: 21 July 2009
Accepted: 31 August 2009

Abstract

Synchronization of groups of coupled oscillators with sparse connections are explored. It is found that different topologies of intergroup couplings may lead to different synchronizability. In the strong-coupling limit, an analytical treatment and criterion is proposed to judge the synchronization between communities of oscillators, and an optimal connection scheme for the group synchronization is given. By varying the intergroup and intragroup coupling strengths, different synchronous phases, i.e., the unsynchronized state, intragroup synchronization, intergroup synchronization, and global synchronization are revealed. The present discussions and results can be applied to study the pattern formation and synchronization of coupled spatiotemporal systems.