The Solution Of Two Types Of Higher-order Difference Equations And Its Properties

The study of the system of difiefence equations has played an important role in applied mathema_tics,economics and mathematical biology and so forth.The solutions of difference equations,the stability, the asymptotic behavior,the periodic and the oscillation of the solutions which have been studied are arising a great interest.This paper mainly studies two kinds of solutions and its properties of high order difference equations.Based on the content,this paper is divided into two chapters.Chapter 1 In this chapter,we mainly consider a fifth-order system of difference equations where ?n,bn,cn,?n,?n,?n,n?No,No={0,1,2,3...}and initial values x-t,y-t,t? {1,2,3,4,5}are real numbers,such that an?0,?n?0,n?No. Firstly we ob-tain the expressions of solutions,then we give the the expressions of solutions when {?n),{bn},{cn},{?n},{?n},{?n}are constant.And we show the conditions of the asymp-totic property,periodicity,stability or oscillation.Chapter 2 In this chapter,we mainly consider a sixth-order system of difference equations where ?n,bn,cn,?n,?n,?n,n?No,No={0,1,2,3...}and initial values x-t,y-t,t ? {1,2,3,4,5,6}are real numbers,such that ?n?0,?n?0,n ?No. Firstly we ob-tain the expressions of solutions,then we give the the expressions of solutions when {?n},{bn},{cn},{?n},{?n},{?n}are constant.And we show the conditions of the asymp-totic property,periodicity,stability or oscillation.