Research On Anti-periodic Solutions Of Delayed Cellular Neural Networks Without Assuming Global Lipschitz Conditions

This dissertation is devoted to the existence, stability and involved dynamic behaviors of anti-periodic solutions to two classes of delayed cellular neural network models without Lipschitz conditions for signal transfer function. This dissertation consists of three chapters.Chapter 1 gives a brief introduction to the historical background, status and the up-to-date progress for all the investigated problems together with main results in this dissertation.Chapter 2 concerns the existence, uniqueness and locally exponential stability of the anti-periodic solutions to a class of recurrent cellular neural networks (RCNNS) with time-varying delays and continuously distributed delays. By using the analytic techniques of the inequality, matrix theory and Lyapunov functional method, the Lipschitz conditions for signal function are removed completely. Hence, our results improve and generalize some known ones in the literature.By using the similar techniques as in chapter 2, chapter 3 deals with the existence, uniqueness and exponential stability of the anti-periodic solutions to a class of shunting inhibitory cellular neural networks (SICNNS) with mixed delays which improves some known results in the literature.