一类高阶有理差分方程解的收敛性(英文)  

Convergence of the Solutions of a Higher-order Rational Difference Equation

作　　者：王琦[1] 张更容[2] 曾凡平[3] 陈占和[2] 

机构地区：[1]广西工学院理学院,广西柳州545006 [2]广西大学数学与信息科学学院,广西南宁530004 [3]柳州师范高等专科学校数学系,广西柳州545005

出　　处：《应用数学》2012年第3期488-495,共8页Mathematica Applicata

基　　金：Supported by the Natural Science Foundation of China(11161029);the Natural Science Foundation of Guangxi(2010GXNSFA013109,2010GXNSFA013106);the Natural Science Foundation of Guangxi University of Technology(1166218)

摘　　要：本文考查下列高阶有理差分方程xn+1=(α+B1xn-1+B3xn-3+…+B2k+1xn-2k-1)/(A+B0xn+B2xn-2+…+B2kxn-2k,),n=0,1,…,其中k是非负整数,参数α,A,Bi,i=0,1,2,…,2k+1和初始值x-2k-1,x-2k,x-2k+1,…,x0是非负实数.给出充分条件,在此条件下当且仅当∑k+1i=1B2i-1=A时,方程的每个解收敛于方程的一个二周期解.This paper is concerned with the following higher-order rational difference equation.. where k is a non-negative integer, the parameters a ,A, Bi, i = 0,1,2,..., 2k ＋ 1 and the initial condi- tions x0 are non-negative real numbers. We give the sufficient condition under which every non-negative solution of the equation converges to a period-two solution of the equation

关 键 词：差分方程 收敛性 二周期解 有界性 

分 类 号：O175.7[理学—数学]