Research On Periodicity Properties For Some Classes Of Max-type Difference Equation Systems

This dissertation consists of five chapters,its concern focuses on the periodicity properties of some classes of max-type difference equation systems by means of the iteration and mathematical induction.The first chapter is the preface,which describes the studying background and current situation of max-type difference equation.It also presents some general concepts and fundamental knowledge of max-type difference equations.In the second chapter,we investigate the four-periodic solutions of the second-order max-type difference equation with variable coefficients as the following where n ? N,{An}n?N and {Bn}nCN are two-periodic positive sequences,and the initial values u0=?,u-1=?,v0=?,v-1=??(0,+?).We pay our attention in the third chapter to discussing the second-order max-nin-type difference equation with variable coefficients as the following where n?N,{An}n?N and {Bn}n?N are positive real sequences,and the initial values x-1=?,x0=?,y-1=?,y0=? are real numbers.We obtain the general solutions of the system,and the four-periodic solutions are gained when the coefficients satisfy the certain conditions.In the fourth chapter,we mainly focus on studying the third-order max-type difference equation with constant coefficients as the following where n N,A?R,and the initial values x-2,x-1,x0,y-2,y-1,y0 are arbi-trary non-zero constants.The eventually three?periodic solutions of the system are obtained under the certain conditions.This stress in the fifth chapter is to discuss the eventually three?periodic solu?tions of the third-order max-type difference equation with constant coefficients as the following where n?N,A?R,and the initial values x-2,x-1,x0,y-2,y-1,y0 are arbitrary non-zero constants.All of the above researches are accompanied with computer simulations.The experimental results not only illustrate the periodicity behavior of the solutions,but also validate the presented results.