The Stability Analysis For General BAM Nerual Networks With Delays

The focus of this thesis is to study the global asymptotic stability,global ex-ponential stability of general BAM neural networks with delays,and the continuity of equilibrium point which dependent on the parameters.The main points are or-ganized as follows:Firstly, the background and the motivation for the study of general BAM neural networks with delays are presented,and some general research methods are introduced in brief.And it must be pointed out that we just require that activation function is Lipschitz continuous,which is less conservative and less restrictive than much of previous research.Secondly, we obtained a sufficient condition ensuring the existence and unique-ness of the equilibrium point of general BAM neural networks with delays by using topological degree theory,and we also have a sufficient condition ensuring the global exponential stability of general BAM neural networks with delays by constructing a Lyapunov functional.Thirdly, by using topological degree theory and M-matrix theory,we obtained another sufficient conditions ensuring the existence and uniqueness of the equi-librium point of general BAM neural networks with delays,and by constructing a Lyapunov-Krasovskii functional we have a sufficient conditions ensuring the global asymptotic stability of general BAM neural networks with delays.Fourthly, by constructing a homeomorphism map,a proper Lyapunov-Krasovskii functional,and by using the properties of M-matrix, we discuss the global asymp-totic stability of general BAM neural networks with delays while the parameters float at intervals,and the continuity of equilibrium point which dependent on the parameters of the system is also investigated.At last, numerical simulation is given to support the obtained results in the back of each chapter.