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Báo cáo hoa học: "Research Article Dynamic Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Dynamic Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 410823 18 pages doi 10.1155 2009 410823 Research Article Dynamic Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays Jie Pan1 2 and Shouming Zhong1 1 College of Applied Mathematics University of Electronic Science and Technology of China Chengdu Sichuan 610054 China 2 Department of Mathematics Sichuan Agricultural University Yaan Sichuan 625014 China Correspondence should be addressed to Jie Pan guangjiepan@163.com Received 13 June 2009 Revised 20 August 2009 Accepted 2 September 2009 Recommended by Tocka Diagana Stochastic effects on convergence dynamics of reaction-diffusion Cohen-Grossberg neural networks CGNNs with delays are studied. By utilizing Poincare inequality constructing suitable Lyapunov functionals and employing the method of stochastic analysis and nonnegative semimartingale convergence theorem some sufficient conditions ensuring almost sure exponential stability and mean square exponential stability are derived. Diffusion term has played an important role in the sufficient conditions which is a preeminent feature that distinguishes the present research from the previous. Two numerical examples and comparison are given to illustrate our results. Copyright 2009 J. Pan and S. Zhong. 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. 1. Introduction In the recent years the problems of stability of delayed neural networks have received much attention due to its potential application in associative memories pattern recognition and optimization. A large number of results have appeared in literature see for example fl-14 . As is well known a real system is usually affected by external perturbations which in many cases are of great uncertainty and hence may be treated as random .