The Exponential Stability For Two Classes Of Bidirectional Associate Memory Neural Networks With Reaction Diffusion

Bidirectional associate memory(BAM) neural networks have extensive applications in pattern recognition, signal processing, associative memories and so on. However, these applications greatly depend on the dynamics of BAM neural networks, especially the exponential stability of equilibrium point. In some classes of BAM neural networks, the state variables of neurons are dependent on not only time but also space. So reaction-diffusion terms should be taken into account to BAM neural networks. Therefore, the effect of reaction-diffusion is considered when studying the exponential stability for BAM neural networks. The main purpose of this paper is to study the exponential stability for BAM neural networks with reaction-diffusion. It includes the following three parts:Firstly, this part has introduced the background of BAM neural networks, as well as the research status of BAM neural networks at home and abroad.Secondly, the exponential stability for BAM neural networks with time-varying delays and reaction-diffusion terms is studied. By using some inequality techniques, graph theory as well as Lyapunov stability theory, a systematic method of constructing global Lyapunov function is provided. Furthermore, two different kinds of sufficient principles are derived to guarantee the exponential stability for BAM neural networks. In the end of this chapter, a numerical example is carried out to demonstrate the effectiveness and applicability of theoretical results.Thirdly, the stability set for BAM neural networks with reaction-diffusion terms is investigated. The subset of stability set for BAM neural networks with reaction-diffusion terms is derived by combining inequality techniques, graph theory and Lyapunov stability theory. Furthermore, this part has shown that the stability set has a close relationship with the topological structure of BAM neural networks by using graph theoretic approach. Finally, a special example is provided to illustrate the feasibility of the main conclusions.