Delay Dynamic Equations on Isolated Time Scales and the Relevance of One-Periodic Coefficients

Abstract

We are motivated by the idea that certain properties of delay differential and difference equations with constant coefficients arise as a consequence of their one-periodic nature. We apply the recently introduced definition of periodicity for arbitrary isolated time scales to linear delay dynamic equations and a class of nonlinear delay dynamic equations. Utilizing a derived identity of higher order delta derivatives and delay terms, we rewrite the considered linear and nonlinear delayed dynamic equations with one-periodic coefficients as a linear autonomous dynamic system with constant matrix. As the simplification of a constant matrix is only obtained for one-periodic coefficients, dynamic equations with one-periodic coefficients are the simplest form compared to the commonly used constant coefficients.

Department(s)

Mathematics and Statistics

Publication Status

Early View: Online Version of Record before inclusion in an issue

Comments

First published: 25 February 2022

Keywords and Phrases

Delay; Dynamic Equations; Periodicity; Stability; Time Scales

International Standard Serial Number (ISSN)

1099-1476; 0170-4214

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2022 Wiley, All rights reserved.

Publication Date

25 Feb 2022

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