一类高阶差分方程的全局吸引性(英文)

Global Attractivity of a Higher-Order Nonlinear Difference Equation

研究了差分方程xn+1=α-(xn-k)/xn,n=0,1,…的有界性,周期性和全局吸引性,其中α为(α>1)的实数,初始条件x-k,…,x0为任意实数,得到方程的平衡点是一个全局吸引子,且其吸引域依赖参数的限制条件.

In this paper,the global attractivity of the nonlinear difference equation xn＋1=α-（xn-k）/xn,n=0,1,… is investigated,where α∈（1,＋∞）,k is a positive integer,and the initial conditions x-k,…,x0 are arbitrary positive real numbers.We show that the unique positive equilibrium of the equation is a global attractor with a basin that depends on certain conditions of the coefficient.