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Delay dynamic equations on isolated time scales and the relevance of one‐periodic coefficients.
- Source :
-
Mathematical Methods in the Applied Sciences . Jul2022, Vol. 45 Issue 10, p5821-5838. 18p. - Publication Year :
- 2022
-
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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *DELAY differential equations
*EQUATIONS
*NONLINEAR equations
*DYNAMICAL systems
Subjects
Details
- Language :
- English
- ISSN :
- 01704214
- Volume :
- 45
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Mathematical Methods in the Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 157265217
- Full Text :
- https://doi.org/10.1002/mma.8141