Study On The Dynamic Properties Of Several Exponential Difference Equations

Difference equation is an important branch of dynamical systems in applied mathematics research,and it is also an important tool to describe discrete-time systems in the real world.In recent years,with the establishment of qualitative analysis theory of differential equations,the dynamic properties of difference equations have also been extensively studied.At the same time,the application of difference equation is closely related to the research of natural science,and has been widely applied in important fields such as bioengineering,economy and finance,automatic control and design,and medicine,among which exponential difference equations appear in population dynamics.Although it is difficult to study dynamics involving exponential difference equations,it is very interesting.On this basis,this dissertation studies the dynamic properties of three exponential types of systems of difference equations.In the first part,we consider the global asymptotic stability of the equilibrium points of three special forms of exponential types of systems of difference equations.The research process is mainly divided into two parts.First,the existence and uniqueness of the equilibrium point of each system and the convergence of positive solutions are discussed,and then the asymptotic stability of the equilibrium point is discussed.In the second part,the dynamic properties of three special forms of a three-species biological model which can be used as an interaction under the influence of influence factors in recent two years and has exponential self-regulation function are studied.Firstly,the boundedness and persistence of positive solutions are studied respectively.Secondly,the existence and uniqueness of equilibrium points,local asymptotic stability and global asymptotic stability of each system are discussed.In the third part,we discuss the dynamic properties of three special forms of systems that can be used as a three-species exponential types of systems of difference equations under the influence of nearly several years influence factors.The study also includes the boundedness and persistence of positive solutions for each system,as well as the existence and uniqueness of equilibrium points,local asymptotic stability and global asymptotic stability.