The Dynamical Behavior Of Two Classes Of Rational Difference Equations

As we all know, as a special class of nonlinear difference equations, the dynamical behavior of rational difference equation is more complex. Meanwhile, with the rapid development of science and technology, all kinds of mathematical model described by the rational difference equation were put forward in application fields such as biology, electron and engineering. Therefore, it is important to study the dynamical behavior of rational difference equation for both theoretic and applied values.In this paper, we mainly discuss the dynamics of two types of rational difference equations, which include the formulas of the solutions with nonzero real number initial conditions, periodicity of the solutions, boundedness and persistence, existence and uniqueness of positive equilibrium, local and global stability of positive equilibrium point, and rate of convergence of positive solutions of rational difference equations.In chapter 1, we introduce the research background and current status of rational difference equations, and give the basic definitions and theories for our discussions.In chapter 2, we study a class of second-order rational difference equation. First, we discuss the boundedness and persistence of the solutions. Next, we obtain the existence of the unique positive equilibrium point, whose local and global asymptotic stability are also studied. Further, we analyze the rate of convergence of positive solutions to the unique positive equilibrium point and periodicity of the solutions. At last, we illustrate our results by the numerical simulation.In chapter 3, we consider a class of third-order rational difference equation. The formulas of the solutions with nonzero real number initial conditions are obtained. Fur-ther, periodic solution of difference equations is discussed.