The Research On Dynamical Behaviour Of Some Kinds Of Rational Difference Equations

Recently, difference equation theory and application research have been the hot issue on the international.This paper aims to study the global asymptotical stability of the nonlinear rational difference equations, which are some "Open Problems and Conjectures"given by Ladas.The content of the dissertation is divided into four chapters, namely:In chapter1, we first simply and primary introduce the historical background and the progress of the difference equations.At the same time, we list the related knowledge of the difference equation,which are commonly used in this paper.In chapter2,on the basis of expanding the class of the rational difference equations proposed by Ladas,and applying of the boundedness of the equation,we prove the unique positive equilibrium point of the equation is globally asymptotically stable.In chapter3, the following fourth-order rational difference equation is considered in detail.By analysising the regular of the rule,we prove the positive equilibrium point of the equation is globally asymptotically stable.In chapter4, using the methods of convergence theorem, we investigate the global behavior of all solutions and periodicity for the rational difference equation. Zhao Yinfeng(Applied Mathematics) Directed by Liao Maoxin...