The Study Of The Asymptotic Behavior Of Solutions For Several Classes Of Difference Equations

Difference equations are key tools to describe the evolution of certain phenomena over the course of discrete time,which are not only widely used in various branches of mathematics,but also can be applied to medicine,physics,economics,population dynamics,neural networks,numerical analysis,control theory and other sciences with the rapid development of computers.In recent years,difference equations of exponen-tial form have a broad application background and numerous potential applications in biology.This thesis consists of three chapters,which mainly focuses on the stabili-ty and the boundedness,persistence,convergence of solutions of systems of difference equations of exponential form.Chapter 1 deals with the research background and development process of differ-ence equations,and contains the significance of the research on systems of difference equations of exponential form.It also includes the basic concepts and some relevant theories of difference equations involved in this thesis.In chapter 2,we study the dynamical behavior of a class of system of exponential difference equations which can be considered as a two-species discrete-time biological model.More precisely,we investigate the existence of a unique nonnegative equilibri-um,the boundedness,persistence and the global asymptotic behavior of the positive solutions of the system of exponential difference equations.The emphasis in the third chapter is to study the dynamics of two special cases of a class of system of exponential difference equations.More precisely,we study the existence of the unique positive equilibrium of the exponential system.In addition,we investigate the boundedness,the persistence and the convergence of the positive solutions of the system.Finally we study the global asymptotic behavior of the positive solutions of the exponential system.