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 exponential stability for cellular neural networks with mixed delays, as well as global asymptotic stability analysis of nonlinear differential equations in hybrid bidirectional associative memory neural networks with distributed time-varying delays. A novel criterion for global asymptotic stability results of delayed Hopfield 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 mixed delays, where we consider cellular neural networks is nonlinear systems, these improve or generalize linear systems the results about some literatures. Using ( )pa p ?1 b≤p ? 1a p + bp inequality and some basis theory, along with constructing newer Lyapunov function than which has been adopted in some literature ever, we further study the stability issue of cellular neural networks with mixed delays, and obtain some judging conditions, as well as present some series of sufficient rules.In Chapter 3, We mainly probe into global asymptotic stability analysis of nonlinear differential equations in hybrid bidirectional associative memory neural networks with distributed time-varying delays. By using topological degree theory and M-matrix theory, several sufficient conditions ensuring the existence uniqueness and global asymptotic stability of equilibrium are derived. Improve the results of some literatures.In Chapter 4,By utilizing Lyapunov functional method and the linear matrix inequality approach, we analyze the global asymptotic stability of Hopfield neural networks with time delays. A novel criterion takes the results about some literatures.In Chapter 5, we summarize the content of the article, and go along expecting discussion.