Floquet Theory for Quaternion-Valued Differential Equations

被引：15

作者：

Cheng, Dong ^{[1
]}

Kou, Kit Ian ^{[2
]}

Xia, Yong Hui ^{[3
]}

机构：

[1] Beijing Normal Univ, Res Ctr Math & Math Educ, Zhuhai, Peoples R China

[2] Univ Macau, Fac Sci & Technol, Dept Math, Macau, Peoples R China

[3] Zhejiang Normal Univ, Dept Math, Jinhua, Zhejiang, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2020年 / 19卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Floquet theory; Periodic systems; Quaternion; Non-commutativity; Hill's equation; MATRIX; EULER;

D O I：

10.1007/s12346-020-00355-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：23

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