Floquet Theory for Quaternion-Valued Differential Equations

• Cheng, Dong ^[1] ; Kou, Kit Ian ^[2] ; Xia Yong Hui ^[3]
  1. [1] Beijing Normal University

     Beijing Normal University

     China

     
  2. [2] University of Macau

     University of Macau

     RAE de Macao (China)

     
  3. [3] Zhejiang Normal University

     Zhejiang Normal University

     China

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
• Idioma: inglés
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• Resumen

  • This paper describes the Floquet theory for quaternion-valued differential equations (QDEs). The Floquet normal form of fundamental matrix for linear QDEs with periodic coefficients is presented and the stability of quaternionic periodic systems is accordingly studied. As an important application of Floquet theory, we give a discussion on the stability of quaternion-valued Hill’s equation. Examples are presented to illustrate the proposed results.