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Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 727068, 20 pages
http://dx.doi.org/10.1155/2011/727068
Research Article

Almost Periodic Functions on Time Scales and Applications

Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China

Received 13 March 2011; Accepted 23 May 2011

Academic Editor: Mingshu Peng

Copyright © 2011 Yongkun Li and Chao Wang. 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 first propose the concept of almost periodic time scales and then give the definition of almost periodic functions on almost periodic time scales, then by using the theory of calculus on time scales and some mathematical methods, some basic results about almost periodic differential equations on almost periodic time scales are established. Based on these results, a class of high-order Hopfield neural networks with variable delays are studied on almost periodic time scales, and some sufficient conditions are established for the existence and global asymptotic stability of the almost periodic solution. Finally, two examples and numerical simulations are presented to illustrate the feasibility and effectiveness of the results.