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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 946243, 8 pages
http://dx.doi.org/10.1155/2013/946243
Research Article

Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes

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

Received 5 August 2012; Revised 21 November 2012; Accepted 18 December 2012

Academic Editor: Shukai Duan

Copyright © 2013 Ze Tang and Jianwen Feng. 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.

Abstract

We focus on the cluster synchronization problem for a kind of general networks with nondelayed and delayed coupling. Based on the pinning control scheme, a small fraction of the nodes in each cluster are pinned for successful control, and the states of the whole dynamical networks can be globally forced to the objective cluster states. Sufficient conditions are derived to guarantee the realization of the cluster synchronization pattern for all initial values by means of the Lyapunov stability theorem and linear matrix inequalities (LMIs). By using the adaptive update law, relative smaller control gains are obtained, and hence the control cost can be substantially lower. Numerical simulations are also exploited to demonstrate the effectiveness and validity of the main result.