The Research Of Existence And Stability On The Anti-periodic Solutions Of Neural Networks

Anti-periodic solution, as a special case of periodic solution, has an important research value in dynamic behavior of the neural networks. Based on the Lyapunov functional method, the linear matrix inequality technique, Leray-Schauder degree theory in Banach Space, and the uniform convergence theorem, this paper studies the anti-periodic dynamical behavior of three types of neural networks, and discusses the existence, uniqueness and stability of the anti-periodic solutions of such neural networks.This paper is divided into five chapters:Chapter 1 introduces the historical background and the research review of the neural networks. It points out the significance of studying the anti-periodic solutions of the neural networks, and analyzes the current research status.Chapter 2 gives some necessary related definitions and Lyapunov stability theory.Chapter 3 studies the anti-periodic solutions of Hopfield neural networks (HNNs), with unbounded and non-Lipschitz activation functions. It works out the criterion of the unique existence of anti-periodic solutions and global asymptotical stability.Chapter 4 investigates anti-periodic solutions of neural networks with time-varying delays and continuously distributed delays, and establishes new criterions for the uniqueness, existence and global exponential stability.Chapter 5 proves the existence of anti-periodic solutions for BAM neural networks with unbounded activation functions.At last, a conclusion and a prospect of future research are maded.