Stability Analysis Of BAM Neural Networks

This paper studies three classes of BAM neural networks with delays:BAM neural networks with distributed delays, BAM neural networks with time-varying coefficients and distributed delays, Cohen-Grossberg BAM neural networks with delays by using Homeomorphism theory and degree theory. Some new sufficient conditions are derived for the existence, uniqueness and global asymptotic stability (or global exponential stability) of the equilibrium point (or periodic solution) for systems. The paper is divided into four chapters. Main contents are as follows:In Chapter1, we introduce the research progress of BAM neural network and prior knowledge.In Chapter2, we mainly discuss a class of BAM neural networks with distributed delays. By applying Homeomorphism theory, some sufficient conditions are derived for the existence, uniqueness of the equilibrium point for the system. Then applying linear matrix inequality technique and Lyapunov functional, some new sufficient conditions are derived for the global asymptotic stability of the equilibrium point for the system.In Chapter3, we investigate a class of BAM neural networks with time-varying co-efficients and distributed delays. New sufficient conditions are derived for the existence, uniqueness of the periodic solution for the system by using coincidence degree theory, M-matrix theory and inequality technique; By constructing corresponding Lyapunov function, we obtain some new sufficient conditions for the global exponential stability results of the periodic solution for the system.In Chapter4, we discuss a class of Cohen-Grossberg BAM neural networks with delays. By the similar way used in chapter3, some new sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of the equilibrium point for the system.In order to illustrate the effectiveness of the method, we give a example in the back of each section to verify the effectiveness of the obtained results.