TY - JOUR

T1 - Asymptotic dynamics of hermitian riccati difference equations

AU - Kuo, Yueh Cheng

AU - Lin, Huey Er

AU - Shieh, Shih Feng

N1 - Publisher Copyright:
© 2021 American Institute of Mathematical Sciences. All rights reserved.

PY - 2021/4

Y1 - 2021/4

N2 - In this paper, we consider the hermitian Riccati difference equa- tions. Analogous to a Riccati differential equation, there is a connection be- tween a Riccati difference equation and its associated linear difference equation. Based on the linear difference equation, we can obtain an explicit representa- tion 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.

AB - In this paper, we consider the hermitian Riccati difference equa- tions. Analogous to a Riccati differential equation, there is a connection be- tween a Riccati difference equation and its associated linear difference equation. Based on the linear difference equation, we can obtain an explicit representa- tion 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.

KW - Asymptotic behavior

KW - Hermitian Riccati difference equations

KW - Riccati difference equations

KW - Riccati differential equations

KW - The extended solution

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U2 - 10.3934/dcdsb.2020365

DO - 10.3934/dcdsb.2020365

M3 - Article

AN - SCOPUS:85101356863

SN - 1531-3492

VL - 26

SP - 2037

EP - 2053

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 4

ER -