Global Dynamical Behaviors Of Static Neural Network Models With S-type Distributed Delays

Artificial neural networks are a very active research area in these years. People believe that neural networks can be applied in many fields. Recurrent neural networks, which can be applied in associative memory, optimization computation, robust control, etc., are an important type of neural networks. They have attracted many scholars'interests. Basing on the difference of basic variables, the mathematical models of recurrent neural networks can be divided into two types—local field neural network models and static neural network models. Most current reseaches about recurrent neural networks focused on the local field models, few paied attention to the static models. However, static models are widely representive. Many useful neural networks are modeled as static models. It is important to investigate the static models. In this paper, the author generalizes the static models and investigates their global dynamical behaviors. The results in this paper include two parts-theory and application:Theory In this part, with fixed point theory, Lyapunov functional and inequation estimation, the following problems are investigatedGlobal asymptotic robust stability of static neural network models with S-type distributed delays on finite intervals.Global attractivity of the periodic solution of static neural network models with S-type distributed delays on finite intervals.Global asymptotic stability of static neural network models with S-type distributed delays on infinite intervals.Global asymptotic stability of general recurrent neural network models with S-type distributed delays on infinite intervals. Application Solving functional differential equations and neural network simulation with Matlab are introduced in this part.The paper is divided into 4 chapterts. Chapter 1 introduces the general knowledge, classification, properties, history and current status of neural networks at first. Then is the relative knowledge about recurrent neural networks and some preliminaries of this paper.Chapter 2 is the part of theory. It consists of two sections. InSection 2.1, the models are generalized as static models with S-type distributed delays on finite intervals. Global asymptotic robust stability and existence of global periodic attractor are investigated. Some examples are given to show that the models are highly general. InSection 2.2, the global asymptotic stability of static models with S-type distributed delays on infinite interval is studied. Moremovr, the models...