Issue
EPL
Volume 87, Number 5, September 2009
Article Number 50006
Number of page(s) 5
Section General
DOI http://dx.doi.org/10.1209/0295-5075/87/50006
Published online 24 September 2009
EPL, 87 (2009) 50006
DOI: 10.1209/0295-5075/87/50006

Synchronization of groups of coupled oscillators with sparse connections

Zhigang Zheng1, Xiaoqin Feng1, Bin Ao2 and Michael C. Cross1, 3

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

zgzheng@bnu.edu.cn

received 21 July 2009; accepted in final form 31 August 2009; published September 2009
published online 24 September 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.

PACS
05.45.Xt - Synchronization; coupled oscillators.
89.75.-k - Complex systems.

© EPLA 2009