Periodic Solutions in a Simple Delay Differential Equation

被引：2

作者：

Ivanov, Anatoli ^{[1
]}

Shelyag, Sergiy ^{[2
]}

机构：

[1] Penn State Univ, Dept Math, Dallas, PA 18612 USA

[2] Flinders Univ S Australia, Coll Sci & Engn, Adelaide, SA 5042, Australia

来源：

MATHEMATICAL AND COMPUTATIONAL APPLICATIONS | 2024年 / 29卷 / 03期

关键词：

delay differential equations; periodic negative feedback; slowly oscillating solutions; periodic solutions; piecewise constant nonlinearities; explicit piecewise affine solutions; reduction to interval maps; CHAOS;

D O I：

10.3390/mca29030036

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：14

共 22 条

[1] Periodic solutions in general scalar non-autonomous models with delays [J].