Types Of Discrete Neural Network Model For The Asymptotic Cyclical

In this thesis, we study the asymptotic behavior and periodicity for four classes of discreted neural network models,where the function f iswhere is a given constant.In the first chapter, we introduce the historical backgraound of problems which will be investigated and the main works of this paper.In chapter 2, we study the models (1) and (2). For equation (1), our conclusionsare as follows; the equation has an unique global attractor when b or athere is the periodic solution whose minimal positive period is m+1 when (the definitions of b and B are is this paper); and when a b are the other values, the solution of (1) is convergent. For equation (2), wehave conclusions that the equation has an unique global attractor when or athere is periodic solution with minimal positive period m+1 when a or a(the definitions of a and Am are in this thesis); and when a,6 are the other vaues, the solution of (2) is convergent .The model (3) has been studied in chapter 3. When b or a or aequation (3) has only one global attractor. If the initial value is solution exists when In this chapter we also consider the problems of periodi and asymptoticbehavior then b is in the other conditions and obtain a series of conclusions. When ab we have some similar answers in section 2.We study model (4) in chapter 4. The unique global attractor of equation (4) exists when or a>0. While the equation has periodic solutions.We also anaylsis the other conditions and obtain some conclusions of asymptotic behavior and periodicity of equation (4).