一类有理差分方程的全局吸引性  

The Global Attractivity of a Rational Difference Equation

作　　者：袁晓红[1] 晏兴学[1] 王仁虎[1] 

机构地区：[1]河西学院数学系,甘肃张掖734000

出　　处：《河西学院学报》2010年第2期1-8,28,共9页Journal of Hexi University

基　　金：甘肃省教育厅科研项目(0709-03);甘肃省教育厅科研项目(0809B-04)

摘　　要：研究了一类有理差分方程yn+1=(pyn+yn-k/pyn+yn-k),n∈N0,p*q*y-k…,y-1,y0∈[0,∞)的全局渐近稳定性.证明了该方程的正平衡点在一定条件下是全局渐近稳定的.特别地,利用更为简单的方法,证明了当p>q时,该方程的正平衡点是一个全局吸引子.从而证明了M.Kulenovic和G.Ladas在文[3]中提出的一个猜想.This paper studies the global asymptotic stability of the difference equation yn＋1=（pyn＋yn-k/pyn＋yn-k）,n∈N0 where p,q ≥ 0are real numbers,,and the initial conditions are nonnegative real numbers such as or or both are positive real numbers.We prove that the positive equilibrium of the difference equation is globally asymptotically stable under certain conditions.In particular,by using a simpler method,we show that the unique positive equilibrium of this difference equation is a global attrator if p q,and the result gives the affirmative answer to Conjecture 6.10.5 in[3] proposed by M.Kulenovic and G.Ladas.

关 键 词：差分方程 全局吸引子 全局吸引性 全局渐近稳定性 

分 类 号：O175.1[理学—数学]