Stable periodic solutions in scalar periodic differential delay equations

Anatoli Ivanov; Sergiy Shelyag

Archivum Mathematicum (2023)

  • Volume: 059, Issue: 1, page 69-76
  • ISSN: 0044-8753

Abstract

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A class of nonlinear simple form differential delay equations with a T -periodic coefficient and a constant delay τ > 0 is considered. It is shown that for an arbitrary value of the period T > 4 τ - d 0 , for some d 0 > 0 , there is an equation in the class such that it possesses an asymptotically stable T -period solution. The periodic solutions are constructed explicitly for the piecewise constant nonlinearities and the periodic coefficients involved, by reduction of the problem to one-dimensional maps. The periodic solutions and their stability properties are shown to persist when the nonlinearities are “smoothed” at the discontinuity points.

How to cite

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Ivanov, Anatoli, and Shelyag, Sergiy. "Stable periodic solutions in scalar periodic differential delay equations." Archivum Mathematicum 059.1 (2023): 69-76. <http://eudml.org/doc/298970>.

@article{Ivanov2023,
abstract = {A class of nonlinear simple form differential delay equations with a $T$-periodic coefficient and a constant delay $\tau >0$ is considered. It is shown that for an arbitrary value of the period $T>4\tau -d_0$, for some $d_0>0$, there is an equation in the class such that it possesses an asymptotically stable $T$-period solution. The periodic solutions are constructed explicitly for the piecewise constant nonlinearities and the periodic coefficients involved, by reduction of the problem to one-dimensional maps. The periodic solutions and their stability properties are shown to persist when the nonlinearities are “smoothed” at the discontinuity points.},
author = {Ivanov, Anatoli, Shelyag, Sergiy},
journal = {Archivum Mathematicum},
keywords = {delay differential equations; nonlinear negative feedback; periodic coefficients; periodic solutions; stability},
language = {eng},
number = {1},
pages = {69-76},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Stable periodic solutions in scalar periodic differential delay equations},
url = {http://eudml.org/doc/298970},
volume = {059},
year = {2023},
}

TY - JOUR
AU - Ivanov, Anatoli
AU - Shelyag, Sergiy
TI - Stable periodic solutions in scalar periodic differential delay equations
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 059
IS - 1
SP - 69
EP - 76
AB - A class of nonlinear simple form differential delay equations with a $T$-periodic coefficient and a constant delay $\tau >0$ is considered. It is shown that for an arbitrary value of the period $T>4\tau -d_0$, for some $d_0>0$, there is an equation in the class such that it possesses an asymptotically stable $T$-period solution. The periodic solutions are constructed explicitly for the piecewise constant nonlinearities and the periodic coefficients involved, by reduction of the problem to one-dimensional maps. The periodic solutions and their stability properties are shown to persist when the nonlinearities are “smoothed” at the discontinuity points.
LA - eng
KW - delay differential equations; nonlinear negative feedback; periodic coefficients; periodic solutions; stability
UR - http://eudml.org/doc/298970
ER -

References

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