Taiwanese Journal of Mathematics

Time-asymptotic Dynamics of Hermitian Riccati Differential Equations

Yueh-Cheng Kuo, Huey-Er Lin, and Shih-Feng Shieh

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The matrix Riccati differential equation (RDE) raises in a wide variety of applications for science and applied mathematics. We are particularly interested in the Hermitian Riccati Differential Equation (HRDE). Radon's lemma gives a solution representation to HRDE. Although solutions of HRDE may show the finite escape time phenomenon, we can investigate the time asymptotic dynamical behavior of HRDE by its extended solutions. In this paper, we adapt the Hamiltonian Jordan canonical form to characterize the time asymptotic phenomena of the extended solutions for HRDE in four elementary cases. The extended solutions of HRDE exhibit the dynamics of heteroclinic, homoclinic and periodic orbits in the elementary cases under some conditions.

Article information

Taiwanese J. Math., Volume 24, Number 1 (2020), 131-158.

Received: 13 September 2018
Revised: 21 February 2019
Accepted: 23 June 2019
First available in Project Euclid: 5 July 2019

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Zentralblatt MATH identifier

Primary: 15Axx: Basic linear algebra 65L20: Stability and convergence of numerical methods 93C15: Systems governed by ordinary differential equations [See also 34H05] 31B35: Connections with differential equations

Riccati differential equation Hermitian Riccati differential equation Radon's lemma finite escape time phenomenon extended solutions Hamiltonian Jordan canonical form


Kuo, Yueh-Cheng; Lin, Huey-Er; Shieh, Shih-Feng. Time-asymptotic Dynamics of Hermitian Riccati Differential Equations. Taiwanese J. Math. 24 (2020), no. 1, 131--158. doi:10.11650/tjm/190605. https://projecteuclid.org/euclid.twjm/1562313624

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