The Stability Analysis For Two Types Of Delayed BAM Neural Network Models

In this paper, the stability of two types of BAM neural networks with time delays are focused on. Because of its good prospects in application, BAM neural networks are widely used in pattern recognition, signal and image processing, artificial intelligence and biotechnology. However, these applications mainly de-pend on the stability of BAM neural networks. Thus, it is significative to discuss the stability of BAM neural networks. Besides, it can be separated into three chapters.In the first chapter, the research on the background and the significance of the BAM neural networks are introduced. In addition, the history of the development is presented. Meanwhile, some lemmas and notations that will be used in the following article are mentioned, and some definitions are also recommended.In the second chapter, global asymptotic stability of a type of BAM neu-ral networks with distributed delays are detailedly analysed. Based on two-dimensional BAM neural networks with distributed delays have more functions on parallel computing and combinatorial optimization and other fields, so the stability of such two-dimensional networks are mainly discussed. In case that only global Lipschitz conditions are satisfied by the activation functions, a new LMI-based sufficient condition on the existence and uniqueness of the equilibrium point of a type of BAM neural networks with distributed delays is obtained by using degree theory, LMI method, inequalities technique and founding Lyapunov functionals, and the global asymptotic stability of the equilibrium point will be further discussed.In the third chapter, the exponential stability of a type of neutral BAM neural network models is mainly discussed. It is very necessary to study the stability of neutral neural networks, the reason is that not only the effect that the past state have on the present state is considered, but also the one that changes of the past state have on the present state is taken into account. By establishing a LV-operator and using the contraction mapping theorem, some new conditions on the existence and uniqueness of the periodic solution of the model are obtained, also, the exponential stability of the periodic solution will be further studied. For the sake of testing the feasibility of the method used in the paper, in the commensurable chapters, the conclusion can be confirmationed by examples.