In this paper, we study the global asymptotic stability of following system of difference equations with quadratic terms: \(x_{n+1}=A+B\frac{y_{n}}{y_{n-1}^{2}}\), \(y_{n+1}=A+B\frac{x_{n}}{x_{n-1}^{2}}\) where A and B are positive numbers and the initial values are positive numbers. We also investigate the rate of convergence and oscillation behaviour of the solutions of related system.

中文翻译：

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具有二次项的差分方程组的全局渐近稳定性

在本文中，我们研究以下带有二次项的差分方程组的全局渐近稳定性：\（x_ {n + 1} = A + B \ frac {y_ {n}} {y_ {n-1} ^ {2 }} \），\（y_ {n + 1} = A + B \ frac {x_ {n}} {x_ {n-1} ^ {2}} \）其中A和B是正数，并且是初始值是正数。我们还研究了相关系统解的收敛速度和振荡行为。