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 -