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Mathematical Problems in Engineering
Volume 2013, Article ID 736585, 12 pages
http://dx.doi.org/10.1155/2013/736585
Research Article

Adaptive Synchronization of Complex Dynamical Multilinks Networks with Similar Nodes

1School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
2Information Security Center, Beijing University of Posts and Telecommunications, Beijing 100876, China
3National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received 2 May 2013; Accepted 21 May 2013

Academic Editor: Ming Li

Copyright © 2013 Weiping Wang 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.

Abstract

This paper studies the synchronization of complex dynamical networks with multilinks and similar nodes. The dynamics of all the nodes in the networks are impossible to be completely identical due to the differences of parameters or the existence of perturbations. Networks with similar nodes are universal in the real world. In order to depict the similarity of the similar nodes, we give the definition of the minimal similarity of the nodes in the network for the first time. We find the threshold of the minimal similarity of the nodes in the network. If the minimal similarity of the nodes is bigger than the threshold, then the similar nodes can achieve synchronization without controllers. Otherwise, adaptive synchronization method is adopted to synchronize similar nodes in the network. Some new synchronization criteria are proposed based on the Lyapunov stability theory. Finally, numerical simulations are given to illustrate the feasibility and the effectiveness of the proposed theoretical results.