The Stability Of The Neural Network And Generalized Periodic Solution

This thesis describes some important properties of dynamic behaviors of several classes of cellular neural networks models with different delays, which includes the existence, uniqueness and exponential stability of the periodic solutions as well as almost periodic solution. It is consists of six chapters.Firstly, this chapter introduced the produce, the advance and the differential system of cellular neural networks. Then, the preface generalizes the basic theory, derives the meaning of investigating stability and almost periodic solution for cellular neural networks, and sums up the central content of the paper.Global exponential stability of almost periodic solution for cellular neural networks with time-varing delays is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this chapter.Based on the fixed point method, a new sufficient condition is obtained for the existence and uniqueness of almost periodic solution of shunting inhibitory cellular neural networks with time-varying delay. Some previous results are improved and extended in this chapter and two examples are given to illustrate the effectiveness of the new result.The existence, uniqueness and global attractivity are discussed on almost periodic solution of shunting inhibitory cellular neural networks with continuously distributed delays. By using the fixed point theorem, differential inequality technique and Lyapunov functional method, giving the new ranges of parameters, several sufficient conditions are obtained to ensure the existence, uniqueness and global attractivity of almost periodic solution. Compared with the previous studies, our methods are more effective for almost periodic solution analysis of shunting inhibitory cellular neural networks with continuously distributed delays. Some existing results have been improved and extended.Global exponential stability, periodic solution and equilibrium point are investigated for cellular neural networks with reaction-diffusion and time-varying delays by the use of Lyapunov-function. Assume that each output function is bounded and satisfies the Lipschitz condition and some other conditions given by this chapter, a series of results are obtained for the stability and periodic solution, existence and uniqueness and the global exponential stability of an equilibrium point.