Global Stability Analysis Of Two Classes Of Delayed Neural Network Models

In recent years, the investigation and applications of neural networks have beendeveloped rapidly. For their great e?ectiveness on associative memories, optimalcomputation, etc., they have attracted the attention of many experts and scholars.In reality, As the speed of energy and information transmission is finite, time-delayphenomena are often encountered in biological and artificial neural networks, whichcan usually cause creating oscillatory and unstable characteristics. So study globalstability of delayed neural networks has important meaning. On the other hand,the interferer of the system not only come from original value, but also come fromsome uncertain factors which regular e?ect on the system from the outside and theinside, which are often varying according to time and depend on the states of thesystem. Thus, global robust exponential stability for neural network models hasalso been investigated by many scholars in recent years. By means of Lyapunovfunctions theory and matrix theory and using Cauchy inequality technique, weanalyze the global stability of two classes of delayed neural networks systems inthis paper.This thesis is composed of three chapters.In the first chapter, we introduce the background knowledge, the significanceand the history of neural networks, and describe the developments of the problem.At the same time, we introduce the purpose of this paper, and also introduce somemarks, the related theorems and lemmas which will be used in this thesis.In the second chapter, we analyze the global asymptotically stability of aclass of Cohen-Grossberg neural network model with multiple time-varying delay.Through homeomorphism theory, we get the su?cient condition for existence anduniqueness of equilibrium points. By means of Lyapunov Krasovskii functionaland Cauchy inequality technique, we get the su?cient conditions to guarantee theglobal asymptotically stability of systems. In addition, our conditions depend onthe time delay. The proposed results generalize previous work. Two examples arepresented to illustrate the e?ectiveness of our results.Chapter three considers global robust exponential stability of a class of cellularneural network model with time-varying delay. By means of Lyapunov functional and inequality technique, we get the su?cient condition to guarantee the globalrobust exponential stability of the systems, and our conditions are related to thedelay. At last, one example is presented to illustrate the e?ectiveness of our results.