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Discrete Dynamics in Nature and Society
Volume 2013, Article ID 140153, 12 pages
http://dx.doi.org/10.1155/2013/140153
Research Article

Complete Periodic Synchronization of Memristor-Based Neural Networks with Time-Varying Delays

Department of Applied Mathematics, Yanshan University, Qinhuangdao 066001, China

Received 6 April 2013; Revised 4 June 2013; Accepted 8 June 2013

Academic Editor: Zhengqiu Zhang

Copyright © 2013 Huaiqin Wu 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 investigates the complete periodic synchronization of memristor-based neural networks with time-varying delays. Firstly, under the framework of Filippov solutions, by using M-matrix theory and the Mawhin-like coincidence theorem in set-valued analysis, the existence of the periodic solution for the network system is proved. Secondly, complete periodic synchronization is considered for memristor-based neural networks. According to the state-dependent switching feature of the memristor, the error system is divided into four cases. Adaptive controller is designed such that the considered model can realize global asymptotical synchronization. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.