Analysis Of The Stability Of Cellular Neural Networks

Since stability theory has enormous impact on cellular neural networks, in this paper, we mostly probe into the global asymptotic stability and global exponential stability for cellular neural networks with delays, as well as mean square exponential stability and almost surely exponential stability for stochastic cellular neural networks. The paper comprises five chapters.In Chapter 1, the preface generalizes the basic theory of stability, derives the meaning of investigating stability for cellular neural networks, and sums up the central content of the paper.In Chapter 2,we consider cellular neural networks with delays, where we discard the demand that the activation functions must be derivable and only request them to be Lipschitz continuous. Using Halanay inequality and the technique of some basal inequality analysis, along with constructing newer Lyapunov function(functional) than which has been adopted in some literature ever, we ulteriorly study the stability issue of cellular neural networks, and obtain some judging conditions, as well as present some series of sufficient rules.In Chapter 3, we mainly probe into mean square exponential stability and almost surely exponential stability for stochastic delayed neural networks. Its especial instances are stochastic cellular neural networks and stochastic delayed Hopfield neural networks. In the section, we utilize Lyapunov function and Young inequality, providing with delay independent conditions and delay dependent conditions, which improve the results of some literatures.In Chapter 4, we mainly investigate that applying the method of variation of the parameters,constructing corresponding Lyapunov function(functional),using Razum- ikhin ideology and so on, we obtain some sufficient conditions on globally asymptotic stability and global exponential stability of fuzzy cellular neural networks. These improve or generalize the results about some literatures.In the last chapter, we summarize the content of the article, and go along expecting discussion.