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Model. Anal. Inform. Sist., 2016, Volume 23, Number 6, Pages 841–849 (Mi mais544)  

This article is cited in 1 scientific paper (total in 1 paper)

Dynamics of a system of two simplest oscillators with finite non-linear feedbacks

A. A. Kashchenko

P.G. Demidov Yaroslavl State University, 14 Sovetskaya str., Yaroslavl 150003, Russia

Abstract: In this paper, we consider a singularly perturbed system of two differential equations with delay which simulates two coupled oscillators with nonlinear feedback. Feedback function is assumed to be finite, piecewise continuous, and with a constant sign. In this paper, we prove the existence of relaxation periodic solutions and make conclusion about their stability. With the help of the special method of a large parameter we construct asymptotics of the solutions with the initial conditions of a certain class. On this asymptotics we build a special mapping, which in the main describes the dynamics of the original model. It is shown that the dynamics changes significantly with the decreasing of coupling coefficient: we have a stable homogeneous periodic solution if the coupling coefficient is of unity order, and with decreasing the coupling coefficient the dynamics become more complex, and it is described by a special mapping. It was shown that for small values of the coupling under certain values of the parameters several different stable relaxation periodic regimes coexist in the original problem.

Keywords: asymptotics, stability, large parameter, relaxation oscillation, periodic solution.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 2014/258-1875
This work was supported by the Ministry of Education and Science of the Russian Federation (project no. 2014/258-1875).


DOI: https://doi.org/10.18255/1818-1015-2016-6-841-849

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Bibliographic databases:

UDC: 517.9
Received: 01.09.2016

Citation: A. A. Kashchenko, “Dynamics of a system of two simplest oscillators with finite non-linear feedbacks”, Model. Anal. Inform. Sist., 23:6 (2016), 841–849

Citation in format AMSBIB
\Bibitem{Kas16}
\by A.~A.~Kashchenko
\paper Dynamics of a system of two simplest oscillators with finite non-linear feedbacks
\jour Model. Anal. Inform. Sist.
\yr 2016
\vol 23
\issue 6
\pages 841--849
\mathnet{http://mi.mathnet.ru/mais544}
\crossref{https://doi.org/10.18255/1818-1015-2016-6-841-849}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3596165}
\elib{http://elibrary.ru/item.asp?id=27517427}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Kaschenko, “Semeistvo negrubykh tsiklov v sisteme dvukh svyazannykh generatorov s zapazdyvaniem”, Model. i analiz inform. sistem, 24:5 (2017), 649–654  mathnet  crossref  elib
  • Моделирование и анализ информационных систем
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