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 Regul. Chaotic Dyn.: Year: Volume: Issue: Page: Find

 Regul. Chaotic Dyn., 2016, Volume 21, Issue 7-8, Pages 811–820 (Mi rcd227)

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

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

DOI: https://doi.org/10.1134/S1560354716070042

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MSC: 37G15, 34C23
Accepted:20.12.2015
Language:

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
\Bibitem{Kas16} \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 \mathnet{http://mi.mathnet.ru/rcd227} \crossref{https://doi.org/10.1134/S1560354716070042} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000403091800004} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85016076616}