Floquet Theory for Quaternion-valued Differential Equations

Dong Cheng; Kit Ian Kou; Yong Hui Xia

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Floquet Theory for Quaternion-valued Differential Equations

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arxiv 1902.09800 v1 pith:MM5A2EB5 submitted 2019-02-26 math.CA

Dong Cheng , Kit Ian Kou , Yong Hui Xia This is my paper

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keywords floquetquaternion-valuedtheorydifferentialequationsperiodicpresentedqdes

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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.

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