Explicit Periodic Solutions in a Delay Differential Equation
Dynamical Systems
2024-02-14 v1
Abstract
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known idea of reduction to interval maps is used in the case under consideration, when both the defining nonlinearity and the periodic coefficient are piece-wise constant functions. The stable periodic dynamics persist under a smoothing procedure in a small neighborhood of the discontinuity set. This work continues the research in recent paper [7] on stable periodic solutions of differential delay equations with periodic coefficients.
Cite
@article{arxiv.2402.08197,
title = {Explicit Periodic Solutions in a Delay Differential Equation},
author = {Anatoli Ivanov and Sergiy Shelyag},
journal= {arXiv preprint arXiv:2402.08197},
year = {2024}
}