Abstract
A simple-form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback coefficient. The periodic solutions are built explicitly in the case with piecewise constant nonlinearities involved. The periodic dynamics are shown to persist under small perturbations of the equation, which make it smooth. The theoretical results are verified through extensive numerical simulations.
| Original language | English |
|---|---|
| Article number | 36 |
| Number of pages | 14 |
| Journal | Mathematical and Computational Applications |
| Volume | 29 |
| Issue number | 3 |
| Early online date | 12 May 2024 |
| DOIs | |
| Publication status | Published - Jun 2024 |
Keywords
- delay differential equations
- explicit piecewise affine solutions
- periodic negative feedback
- periodic solutions
- piecewise constant nonlinearities
- reduction to interval maps
- slowly oscillating solutions