Time-asymptotic dynamics of Hermitian Riccati Differential Equations

Yueh Cheng Kuo, Huey Er Lin, Shih Feng Shieh

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)131-158
Number of pages28
JournalTaiwanese Journal of Mathematics
Volume24
Issue number1
DOIs
Publication statusPublished - 2020 Feb

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Keywords

  • Extended solutions
  • Finite escape time phenomenon
  • Hamiltonian Jordan canonical form
  • Hermitian Riccati differential equation
  • Radon’s lemma
  • Riccati differential equation

ASJC Scopus subject areas

  • Mathematics(all)

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