In this paper, we consider the hermitian Riccati difference equations. Analogous to a Riccati differential equation, there is a connection between a Riccati difference equation and its associated linear difference equation. Based on the linear difference equation, we can obtain an explicit representation for the solution of the Riccati difference equation and define the extended solution. Further, we can characterize the asymptotic state of the extended solution and the rate of convergence. Constant equilibrium solutions, periodic solutions and closed limit cycles are exhibited in the investigation of asymptotic behavior of the hermitian Riccati difference equations.

中文翻译：

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厄米Riccati差分方程的渐近动力学。

在本文中，我们考虑了埃尔米特Riccati差分方程。类似于Riccati微分方程，Riccati差分方程与其关联的线性差分方程之间存在联系。基于线性差分方程，我们可以得到Riccati差分方程解的显式表示，并定义扩展解。此外，我们可以描述扩展解的渐近状态和收敛速度。在研究埃尔米特Riccati差分方程的渐近行为时，展示了恒定平衡解，周期解和封闭极限环。