一类高阶非线性差分方程的吸引性

The Attractivity of a Class of Higher Order Nonlinear Difference Equations

在文献[1-2]的基础上,研究了非线性差分方程xn+1=a-bxpn-k/A-x2n的全局稳定性和正解的周期性,其中a,A为非负实数,b为正实数,k,p∈{1,2,…},p≥2.证明了该方程的一个正平衡点是一个全局吸引子,并给出了相应的吸引域.

On the basis of literature ,we study the global stability and the periodic character of the positive solution of the difference equations xn＋1=a-bxn-k^p/A-xn^2,where a,A are nonnegative real number,b is positive real number and k,p∈{1,2,…},p≥2.We show that the positive equilibrium of the equations is a global attractor with a basin that depends on certain conditions posed on the coefficients by analysis method.