Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 624619, 12 pages
doi:10.1155/2010/624619
Research Article

Existence and Global Exponential Stability of Equilibrium Solution to Reaction-Diffusion Recurrent Neural Networks on Time Scales

Kaihong Zhao1,2 and Yongkun Li1

1Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China
2Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, China

Received 30 March 2010; Accepted 13 July 2010

Academic Editor: Francisco Solis

Copyright © 2010 Kaihong Zhao and Yongkun Li. 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

The existence of equilibrium solutions to reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales is proved by the topological degree theory and M-matrix method. Under some sufficient conditions, we obtain the uniqueness and global exponential stability of equilibrium solution to reaction-diffusion recurrent neural networks with Dirichlet boundary conditions on time scales by constructing suitable Lyapunov functional and inequality skills. One example is given to illustrate the effectiveness of our results.