Dynamic Behaviors Of Two Kinds Of Rational Diference Systems

In recent years,with the establishment of differential mathematical models to solve practical problems in the fields of biology,economics,physics,medicine,etc.,the study of difference equations has become very important.In this paper,the relevant theoretical knowledge of difference equations is used to study the dynamic behavior of two types of rational difference systems,and some conclusions are obtained.Further,MATLAB is used to verify the correctness of the conclusions.In Chapter 1,we introduce the research background and research significance of rational difference systems.In Chapter 2,we give some basic definitions and preliminary knowledge related to this article.In Chapter 3,we study the dynamic behaviors of a class of three-dimensional and m+1-order rational difference systems.For A>1,the boundedness of the positive initial solution sequence of the system is analyzed,and the the existence,stability and global attractiveness of equilibrium points are investigated.Especially,when A=1 and m is even numbers,the existence of order-2 periodic solutions is obtained.Finally,the conclusions are simulated by using MATLAB.In Chapter 4,we study the dynamic behaviors of a class of two-dimensional and third-order rational difference system.Firstly,in the case of r<1,s<1,the bound-edness of the solution sequence {xn,yn} related to the initial value is obtained.The global asymptotical stability of the trivial equilibrium point of the system is studied,and the convergence rate analysis is analyzed.Meanwhile,the nonexistence of the posi-tive equilibrium point is held.Secondly,in the case of r>1,s>1,especially,when the initial value meets certain conditions,the convergence of the solution sequence {xn,yn}is studied,and the unstability of the trivial equilibrium point and positive equilibrium point is obtained.Thirdly,in the case of r>1,s<1 or r<1,s>1,the convergence of solution sequence {xn,yn} of system is revealed.Further,in the case of r>1,s=1 or r=1,s>1,the boundary equilibrium point of the system is not hyperbolic.Finally,the conclusions are simulated by using MATLAB.In Chapter 5,we summarize our works,and point out the deficiencies in the thesis The direction of the next research work is followed.