# American Institute of Mathematical Sciences

## Asymptotic dynamics of hermitian Riccati difference equations

 1 Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, 811, Taiwan 2 Department of Mathematics, National Taiwan Normal University, Taipei 116, Taiwan

* Corresponding author: Huey-Er Lin

(dedicated to Prof. Sze-Bi Hsu in appreciation of his inspiring ideas)

Received  October 2020 Revised  November 2020 Published  December 2020

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.

Citation: Yueh-Cheng Kuo, Huey-Er Lin, Shih-Feng Shieh. Asymptotic dynamics of hermitian Riccati difference equations. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020365
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