Stability Studies Of Two Classes Of Neural Network With Time Delays

The research of dynamic character of the neural network system has promoted the development of computer science, artificial intelligence and pattern recognition areas, and it has important scientific significance, involving complex calculations and intelligent retrieval, image recognition, intelligent monitoring and control of industrial production, national defense, medicine and other fields has important application value. And the research for the stability of neural networks has great significance. This paper is based on Lyapunov stability theory to study two types of time-delay neural network model. This paper obtained some criterions of equilibrium existence, uniqueness and stability. This paper is divided into four chapters.Chapter1is the Introduction, focuses primarily on the history and development of neural networks, and research status, and study the significance of the stability of time delay neural networks; the models of neural networks studied in this paper; Lyapunov stability theory; and the main work in this paper.Chapter2, the delay Cohen-Grossberg neural network stability problem is studied, and obtain the delay Cohen-Grossberg neural network existence and uniqueness of equilibrium point of the criterion by the use of homeomorphism theory; and by constructing new Lyapunov-Krasovskii function, using M-matrix knowledge, proposed and proved delay Cohen-Grossberg neural networks of the new global exponential stability criterion; Finally, The effectiveness of the proposed results in this chapter is demonstrated in numerical examples, and comparing the previous literature to verify the conclusions of this paper has less conservative, than has been the literature of the relevant results.Chapter3, stability of stochastic reaction-diffusion neural networks with Markovian jumping parameters and time delays in the leakage term is studied. By constructing a Lyapunov-Krasovskii function, the use of Schur complement Theorem, Ito inequality, liberty matrix, the matrix inequality, the mean inequality, Jensen inequality and other methods proposed globally asymptotically stable criteria for a class of stochastic reaction-diffusion neural networks with Markovian jumping parameters and time delays in the leakage term; by numerical examples using Matlab numerical simulation to verify the criterion of effectiveness.Chapter4results in this paper are summarized. Stability problem of neural networks is also forecasted and point out the further research direction.