Analysis Of Dynamic Behaviors Of Two Kinds Of Third-order Nonlinear Coupled Rational Difference System

Difference equation is a branch of nonlinear analysis in mathematics,it plays an important role and widely used in many fields of natural(such as economy,power system and ecological system,etc).The research progress of difference equations has developed rapidly in recent years as the research hot in mathematics that makes it has a wider application and people have a deeper understanding of its theories.Two kinds of dynamic behaviors of third-order nonlinear rational difference systems have been discussed by using the basic theoretical knowledge of differential equation and the research achievements of some scholars.and the conclusion was verified through analyzing the numerical results by using MATLAB.In chapter one,the research background and significance of the difference system have been introduced,at the same time,some definitions and preliminary knowledge related to the research content were introduced in this paper,too.In chapter two,the dynamic behaviors of a kind of third-order nonlinear coupled difference system was studyed.By using some basic theories of difference equation,the existence and stability of equilibrium point were discussed,at the same time,The sufficient conditions for the asymptotic stability of the trivial equilibrium point and the unstable equilibrium were given out and the rate of convergence of solution were analyzed,Further,the existence of prime period-two solution of the system is discussed.It proved that there exists the positive prime period-two solution that is not the only in this system,the conclusion were verified through numerical simulation by using MATLAB in the end.In chapter three,By using some basic theories of difference equation,the dynamic behaviors of a kind of third-order nonlinear coupled difference system was discussed.For the system,the existence and stability of the equilibrium point,the rate of convergence of the solution to the equilibrium point and the existence of the prime period-two solution were studied.The paper gave out the sufficient conditions for the asymptotic stability of the trivial equilibrium point and the unstable equilibrium.It is proved that there exists the positive prime period-two solution that is not the only in this system,To verify the theoretical results,by using MATLAB,the numerical simulation verifies the conclusion.In chapter four,this paper was summarized,and pointed out the shortcomings for the paper.At last,a prospect for the future work was made.