Global Stability Analysis For Two Classes Of Recurrent Neural Networks With Delays

Recurrent neural networks with delays, which have been successfully applied in the field of pattern recognition, signal processing, associative memory, optimization problem and so on, are nonlinear information processing systems. Studying the dynamic behavior of the recurrent neural networks with delays, for example, stability, periodic, chaos and so on, has important instruction meanings for the practical applications of the neural networks. In this paper, we mainly study the global exponential stability for the static recurrent neural networks with S-type distributed delays and the global mean square stability of the almost periodic solution for the stochastic cellular neural networks with time-varying delays.This paper is divided into 5 chapters:Chapter 1 introduces the survey of the neural networks, the main works, some basic definitions and theorems.In chapter 2, by using Lyapunov functional, M-matrix and homeomorphic mapping approach, we study the existence, uniqueness and global exponential stability of the equilibrium point for the static recurrent neural networks with S-type distributed delays, and give some sufficient conditions of the existence, uniqueness and global exponential stability. Finally, a number example is given to show the effectiveness of the results.In chapter 3, by using Mawhin's coincidence degree theory and Halanay matrix delays differential inequality, we study the existence and global exponential stability of periodic solution for the static recurrent neural networks with S-type distributed delays, and give the sufficient conditions of the existence and global exponential stability.In chapter 4, by using Holder inequality and fixed point theory, we study the model of the stochastic cellular neural networks with time-varying delays, and give the sufficient conditions of the existence, uniqueness and the global mean square stability of almost periodic solution. The results of related references are extended.In chapter 5, we look forward to the future research directions.