Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 416182, 21 pages
doi:10.1155/2010/416182
Research Article

Adaptive Pinning Synchronization of Complex Networks with Stochastic Perturbations

Xinsong Yang1,2 and Jinde Cao1

1Department of Mathematics, Southeast University, Nanjing 210096, China
2Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, China

Received 14 November 2009; Revised 27 January 2010; Accepted 24 February 2010

Academic Editor: Yong Zhou

Copyright © 2010 Xinsong Yang and Jinde Cao. 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

The adaptive pinning synchronization is investigated for complex networks with nondelayed and delayed couplings and vector-form stochastic perturbations. Two kinds of adaptive pinning controllers are designed. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are developed to guarantee the synchronization of the proposed complex networks even if partial states of the nodes are coupled. Furthermore, three examples with their numerical simulations are employed to show the effectiveness of the theoretical results.