Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 534743, 17 pages
Research Article

Cluster Synchronization for Linearly Coupled Complex Networks with Identical and Nonidentical Nodes

College of Mathematics and Computational Science, Shenzhen University, Guangdong Shenzhen 518060, China

Received 11 April 2012; Accepted 7 July 2012

Academic Editor: Hai L. Liu

Copyright © 2012 Yi Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The cluster synchronization of linearly coupled complex networks with identical and nonidentical nodes is studied. Without assuming symmetry, we proved that these linearly coupled complex networks could achieve cluster synchronization under certain pinning control schemes. Sufficient conditions guaranteeing cluster synchronization for any initial values are derived by using Lyapunov function methods. Moreover, the adaptive feedback algorithms are proposed to adjust the control strength. Several numerical examples are given to illustrate our theoretical results.