Analysis Of Dynamic Behaviors Of Two Kinds Of High-order Rational Difference Systems

Difference equation is an effective method to study the law of variation between discrete variables.In recent decades,the theory and application of difference equation has developed rapidly,especially in the fields of economy,medicine,physics,chemistry biology,military science and so on.At the same time,the theory and application of difference equation helps people to solve many practical problems.Therefore,it has important theoretical significance and application value studying itIn this paper,we discuss the dynamic behaviors of two kinds of special high-order rational difference systems by using basic theories of difference equations.Moreover,the numerical results are simulated and analyzed with MATLAB to verify the correctness of the conclusionsIn chapter one,the research background and significance of the difference system has been introduce,meanwhile,some basic definitions and theories related to the research content are provided in this paper,tooIn chapter two,the dynamic behaviors of a kind of special fourth-order rational difference system are studied including the existence and the 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.Some numerical examples are given to verify the theoretical results.The results show that there exist locally asymptotically stable trivial equilibrium point,unstable positive equilibrium point and not unique prime period-two solution in this system.The theoretical results are verified by the numerical examplesIn chapter three,the dynamic behaviors of a kind of third-order are discussed by using some basic theories of difference equation.Firstly,we discuss the boundedness of the solution and the permanence of system.We obtain the existence of invariant set for such a system.Further,we prove the local stability and global attractivity of the unique equilibrium point,and analysis the rate of convergence of positive solutions.Moreover,we investigate the nonexistence of prime period-two solutions of this system.At last,some numerical examples are given to verify our theoretical results.In chapter four,this paper is summarized,and pointed out the shortcomings for the paper.At last,a prospect for the future work is made.