Copyright © 2012 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 introduce the concept of admitting an exponential dichotomy to a class of linear dynamic equations on time scales and study the existence and uniqueness of almost periodic solution and its expression form to this class of linear dynamic equations on time scales. Then, as an application, using these concepts and results, we establish sufficient conditions for the existence and exponential stability of almost periodic solution to a class of Hopfield neural networks with delays. Finally, two examples and numerical simulations given to illustrate our results are plausible and meaningful.