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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 645214, 18 pages
http://dx.doi.org/10.1155/2012/645214
Research Article

Existence and Global Stability of a Periodic Solution for Discrete-Time Cellular Neural Networks

Department of Automation, Southeast University, Nanjing, Jiangsu 210096, China

Received 9 July 2012; Revised 16 September 2012; Accepted 15 October 2012

Academic Editor: Kwok-Wo Wong

Copyright © 2012 Haijian Shao 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 sufficient condition is developed to obtain the discrete-time analogues of cellular neural network (CNN) with periodic coefficients in the three-dimensional space. Existence and global stability of a periodic solution for the discrete-time cellular neural network (DT-CNN) are analysed by utilizing continuation theorem of coincidence degree theory and Lyapunov stability theory, respectively. In addition, an illustrative numerical example is presented to verify the effectiveness of the proposed results.