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.
Recommended Citation
M. Bohner et al., "Delay Dynamic Equations on Isolated Time Scales and the Relevance of One-Periodic Coefficients," Mathematical Methods in the Applied Sciences, vol. 45, no. 10, pp. 5821 - 5838, Wiley, Jul 2022.
The definitive version is available at https://doi.org/10.1002/mma.8141
Department(s)
Mathematics and Statistics
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
Final Version
File Type
text
Language(s)
English
Rights
© 2023 Wiley, All rights reserved.
Publication Date
15 Jul 2022
