The Research On Dynamics Properties Of Several Types Neural Network Models Of Two Neurons

In this thesis, we describe some important dynamic properties of several class of neural network models of two neurons, which includes asymptotic behavior, the global exponential asymptotic stability,the existence of periodic solution,and also describe the dynamic behaviors of the corresponding discrete models.It is composed of five chapters.In Chapter 1, the background and history of neural networks are briefly reviewed, and the current, situations in the field are generalized, furthermore, we raise some problems which will be investigated.In Chapter 2, two types with McCulloch-Pitts nonlinear neural network models of two neurons are discussed. We study asymptotic behavior and stability of the solution if the absolute' values of threshold values are large and obtain that the two systems have unique equilibrium respectively which is global exponential asymptotic stable. In particular, we obtain necessary and sufficient conditions which guarantee the solutions of the models tend to one of those equilibria respectively in the critical case. In addition, we: illustrate1 by an example that the conclusions contain the results of the emresponding literatures.In Chapter 3, we investigate the existence of periodic solution of a class of the nonlinear neural network of two neurons, by using the analytical technique to find return mapping, we obtain the sufficient conditions for the existence of the isolated periexlie-solution.In Chapter 4, we study the asymptotic behaviors and the global exponential asymptotic stability of two types of discrete-time neural network models of two neurons with positive and negative feedback. The results we get are discrete analogue of the' results of the chapte:r 2.Finally, in Chapter 5, two types of nonlinear neural network moelels of two neurons of two threshold values are considered. Similarly, we; prove that the systems has unique equilibrium respectively and it is global exponential asymptotic stable if the absohite values of threshold values are large, furthermore, necessary and sufficient conditions are obtained for the solutions of the system tending to one of the different equilibria respectively in the critical case.