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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 352826, 8 pages
http://dx.doi.org/10.1155/2013/352826
Research Article

Full Synchronization Studied by a Set of Partitions Connected Together

1School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
2School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China
3Department of Mathematics, Southeast University, Nanjing 210096, China
4Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 9 July 2013; Accepted 22 August 2013

Academic Editor: Qiankun Song

Copyright © 2013 Jianbao Zhang 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

A novel approach is brought forward for synchronization of a clustered network in this paper, the objective of which is twofold. The first one is to study cluster synchronization by analyzing the inner coupling matrices of the individual clusters instead of the one of the whole network. The other is to show that full synchronization can be ensured by several types of cluster synchronization, the partitions of which are connected together. Compared with the classical method for full synchronization, our approach reduces the network size to the cluster size and additionally obtains the thresholds for different types of cluster synchronization. As a numerical example, cluster and full synchronization in a special clustered network are investigated through our approach. It turns out that we obtain the same threshold for full synchronization as the one obtained by the classical method. Numerical simulations confirm the validity of our approach.