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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Abstract

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

Source
Taiwanese J. Math., Advance publication (2019), 28 pages.

Dates
First available in Project Euclid: 5 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1562313624

Digital Object Identifier
doi:10.11650/tjm/190605

Subjects
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

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

Citation

Kuo, Yueh-Cheng; Lin, Huey-Er; Shieh, Shih-Feng. Time-asymptotic Dynamics of Hermitian Riccati Differential Equations. Taiwanese J. Math., advance publication, 5 July 2019. doi:10.11650/tjm/190605. https://projecteuclid.org/euclid.twjm/1562313624


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