Global asymptotic stability of a second-order system of difference equations

In this paper a sufficient condition is obtained for the global asymptotic stability of the following system of difference equations \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x_{n + 1} = \frac{{x_n y_{n - 1}^b + 1}} {{x_n + y_{n - 1}^b }}, y_{n + 1} = \frac{{y_n x_{n - 1}^b + 1}} {{y_n + x_{n - 1}^b }}n = 0,1,2 \ldots$$\end{document} where the parameter b ∈ [0, ∞) and the initial values (xk, yk) ∈ (0, ∞) (for k = −1, 0).