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.


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





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Publication Date

15 Jul 2022