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.
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
Mathematics and Statistics
Keywords and Phrases
delay; dynamic equations; periodicity; stability; time scales
International Standard Serial Number (ISSN)
Article - Journal
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15 Jul 2022