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Regular and Chaotic Dynamics, 2016, Volume 21, Issue 7-8, Pages 811–820
DOI: https://doi.org/10.1134/S1560354716070042 (Mi rcd227) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The Dynamics of Second-order Equations with Delayed Feedback and a Large Coefficient of Delayed Control

Sergey A. Kashchenkoab

a P.G. Demidov Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000 Russia
b National Nuclear Research University (MEPhI), Kashirskoe sh. 31, Moscow, 115409 Russia
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DOI: https://doi.org/10.1134/S1560354716070042
Abstract: The dynamics of second-order equations with nonlinear delayed feedback and a large coefficient of a delayed equation is investigated using asymptotic methods. Based on special methods of quasi-normal forms, a new construction is elaborated for obtaining the main terms of asymptotic expansions of asymptotic residual solutions. It is shown that the dynamical properties of the above equations are determined mostly by the behavior of the solutions of some special families of parabolic boundary value problems. A comparative analysis of the dynamics of equations with the delayed feedback of three types is carried out.
Keywords: delay, feedback, nonlinear dynamics, boundary value problems.
Received: 17.09.2015
Accepted: 20.12.2015
Bibliographic databases:
Document Type: Article
MSC: 37G15, 34C23
Language: English
Citation: Sergey A. Kashchenko, “The Dynamics of Second-order Equations with Delayed Feedback and a Large Coefficient of Delayed Control”, Regul. Chaotic Dyn., 21:7-8 (2016), 811–820
Citation in format AMSBIB
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\by Sergey A. Kashchenko
\paper The Dynamics of Second-order Equations with Delayed Feedback and a Large Coefficient of Delayed Control
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 7-8
\pages 811--820
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\crossref{https://doi.org/10.1134/S1560354716070042}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016076616}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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