The Research On The Periodic Solution And Stability Of Discrete-Time Neural Networks

Stability is a key issue in applications of neural networks. Some neural network models have fixed points, but others have periodic solutions. In applications of neural networks, some request the asymptotical stability of fixed points or periodic solutions, some have higher requirements that they request the exponential stability of fixed points or periodic solutions. In this thesis, we mainly study the existence of periodic solutions of neural networks and the globally asymptotical stability and exponential stability of periodic solutions and fixed points. The paper have four parts:In the first charpter, we present the background and the necessity for the study of neural networks. Then, we introduce some known results of neural networks models. Some basic definitions are given.In the second chapter, we study the existence of periodic solutions for a nonau-tonomous discrete-time neural networks by using the topological degree theory. The mistakes about the conclusion of the existence of fixed points in Weirui zhao's paper [1] have been pointed out and corrected. Then, we present a sufficient condition of globally asymptotical stability in nonautonomous discrete-time neural networks.In the third chapter, we prove the existence of fixed points in discrete-time varying time-delayed cellular neural networks model by using Brouwer theorem. And we give a sufficient condition of globally exponential stability in this model by straight proofing.Finally, in the fourth chapter, we present sufficient conditions of globally exponential stability of discrete-time time-delayed celluar neural networks model by using Brouwer theorem and Lyapunov theory. Our conclusions extend the S.Mohamad's conclusions.