Stability Analysis, Neural Networks With Delay

Neural networks have a wide application in many fields, including signal and image processing, patten recognition, artificial intelligence, some global optimiza-tion problem and so on, and dynamic behavior builds the theoretical basis of the application of this model, thus it is very important to the research for the dynamic characteristics and neural networks. In addition, in practice, delay is inevitable and influences the dynamic behavior of neural networks, especially stability, so the sta-bility of delayed neural networks were widespread concern. In this thesis, we further study the dynamic behavior of three classes of delayed neural networks.In chapter 1, the significance and development of neural networks are firstly introduced. Then, some preliminaries are cited, which include the essential defini-tions, theorems and some inequalities. The main work is summarized at the end of this chapter.In chapter 2, the global exponential stability of the equilibrium points are stud-ied for impulsive neural networks with time-varying and infinite distibuted delays. The sufficient conditions are provided to ensure the global exponential stability of this network by constructing appropriate Lyapunov functional and using linear matrix inequality(LMI). Since this network includes a broad class of models, the obtained results have a wide application. Numerical example not only supports the correctness of the obtained results, but also illustrates that the given conditions are easy to check.In chapter 3, the global asymptotic and exponential stability of the equilib-rium point are discussed for neutral-type static neural networks with time-varying and distributed delays. By using Lyapunov-Krasovskii function and linear matrix inequality(LMI), the sufficient conditions for the global asymptotic and exponen-tial stability of static neural networks are obtained. Since many important neural networks can be transformed into static model, the obtained results not only im-prove corresponding results in the previous literatures and have less conservative, but also have a wide application. Finally, the correctness of the obtained results are illustrated by numerical examples.In chapter 4, the dynamic behavior of a class of delayed one-layer neural network are studied. By the theory of functional differential equations, the existence and uniqueness of the solution of the model are proved. By construting appropriate Lyapunov functional and using the linear matrix inequalities(LMI) method, the sufficient conditions for the global exponential and asymptotic stability of delayed one-layer neural networks are obtained. Since this network can be used to solve a broad class of quadratic programming problems, the obtained results have important theory value and practical significance. Finally, the correctness of the obtained results and the characteristics of this network are illustrated by numerical examples.