多滞量高阶非线性差分方程的全局吸引性

Global Attractivity of Higher-order Nonlinear Difference Equation

研究了差分方程xn+1=(a+bxn)/(A+B xn-k)(C+D xn-l),n=0,1,2,….其中a,b,A,B,C∈(0,∞),D∈[0,∞),k,l是正整数,初值条件x-k,…,x-1及x0是任意正常数的全局吸引性,推广了相关文献的相关结果.

The global attractivity of the nonlinear difference equationXn＋1=a＋bxn/（A＋Bxn-k）（C＋Dxn-t）,n=0,1,2,… is investigated, where a,b, A, B, C E （0, ∞）, D E [- 0, ∞）, k,l are positive integers and the initial conditions xk…,x-t and x0 are arbitrary positive number. It is shown that the unique positive equilibrium of the equation is global attractive.