一类高阶非线性时滞差分方程的全局渐近稳定性

考虑非线性时滞差分方程xnxn+1=α+,n=0,1,2,…,xn-k其中∈(0,+∞),k∈{1,2,…},初始条件x-k,…,x0是任意的正实数.本文获得了非线性时滞差分方程的全α局吸引性,有界性,周期性以及方程在一定条件下的全局渐近稳定性.

Global asymptotic stable of a class of higher order nonlinear delay difference equation

considering the nonlinear delay difference equation xn xn+ 1=α + xn-k, n = 0,1,2, … where,x-k,… ,x0, α∈(0,+ ∞ )and k ∈{1,2, …},we obtain the global attractivity, the boundedness character and the periodic nature of the difference equation, in addition to, we show that the global asymptotic stable of the difference equation under specied conditions.