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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/151281


    Title: Time-asymptotic Dynamics of Hermitian Riccati Differential Equations
    Authors: 郭岳承
    Kuo, Yueh-Cheng;Lin, Huey-Er;Shieh, Shih-Feng
    Contributors: 應數系
    Keywords: extended solutions;finite escape time phenomenon;Hamiltonian Jordan canonical form;Hermitian Riccati differential equation;Radon's lemma;Riccati differential equation
    Date: 2020-02
    Issue Date: 2024-05-24 11:34:31 (UTC+8)
    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.
    Relation: Taiwanese Journal of Mathematics, Vol.24, No.1, pp.131-158
    Data Type: article
    DOI link: https://doi.org/10.11650/tjm/190605
    DOI: 10.11650/tjm/190605
    Appears in Collections:[Department of Mathematical Sciences] Periodical Articles

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