Achieving synchronization of networks by an auxiliary hub

¹  Department of Mathematics, Shanghai University - Shanghai 200444, PRC
²  Department of Neurophysiology, Max Planck Institute for Brain Research - 60528 Frankfurt, Germany
³  Frankfurt Institute for Advanced Studies - 60438 Frankfurt, Germany

Corresponding author: dbhuang@staff.shu.edu.cn

Received: 16 October 2006
Accepted: 23 January 2007

Abstract

In this letter, we study complete synchronization in quite generic networks of coupled oscillators, where both the connectivity topology and coupling mechanism may be arbitrary. We propose a method, i.e., introducing an auxiliary hub which decreases the average path length and meanwhile increases the clustering coefficient of the network, to achieve complete synchronization. We demonstrate that the method is successful in synchronizing some classical network models, which cannot synchronize intrinsically. That is, a network, which itself is impossible to synchronize, can adaptively achieve the complete synchronization by introducing an auxiliary hub. The present results give insights on how the network structure influences the synchronizability and how the synchronization of generic networks can be achieved regardless of their own complexity.