Existence And Exponential Stability Of Periodic Solution And Almost Periodic Solutions Of Cellular Neural Networks With Mixed Delay

In this thesis, we describe some important properties of dynamic behaviors of several class of cellular neural networks models with mixed delay, which includes the existence, uniqueness and exponential stability of the periodic solutions as well as almost periodic solutions. It is consists of three chapters. As the introductions, in Chapter 1, the background of cellular neural networks are briefly addressed, and some notations and definitions are given in this chapter. In Chapter 2, by using the fixed point theorem in Banach space and mathematic analysis, we deduce some sufficient conditions ensuring existence as well as exponential stability of almost periodic solution for a class of shunting inhibitory cellular neural networks with mixed delays.In detail, in part of one,we used differential inequality technique, the fixed point theorem in Banach space and mathematic analysis, we deduce some sufficient conditions ensuring existence as well as global exponential stability of almost periodic solution for a class of shunting inhibitory cellular neural networks with mixed delays;in another part ,we used differential inequality technique, the fixed point theorem in Banach space and mathematic analysis,thinks of the function is unbounded, we deduce some sufficient conditions ensuring existence as well as local exponential stability of almost periodic solution for a class of shunting inhibitory cellular neural networks with mixed delays.In Chapter 3, existence, uniqueness and global exponential stability of the periodic solution of a class of recurrent cellular neural networks with mixed delays are considered. Under the help of matrix theory and fixed point theorem in Banach space, some sufficient conditions ensuring existence, uniqueness as well as global exponential stability of periodic solution are established. Some existing results are improved and extended.