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Journal of Applied Mathematics
Volume 2011, Article ID 735825, 11 pages
http://dx.doi.org/10.1155/2011/735825
Research Article

Periodicity in a Class of Systems of Delay Difference Equations

College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China

Received 5 July 2011; Accepted 23 August 2011

Academic Editor: J. Biazar

Copyright © 2011 Zhijian Wei. 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

We study a system of delay difference equations modeling four-dimensional discrete-time delayed neural networks with no internal decay. Such a discrete-time system can be regarded as the discrete analog of a differential equation with piecewise constant argument. By using semicycle analysis method, it is shown that every bounded solution of this discrete-time system is eventually periodic. The obtained results are new, and they complement previously known results.