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 Mat. Zametki, 2018, Volume 104, Issue 2, Pages 216–230 (Mi mz11704)

Application of the Averaging Principle to the Study of the Dynamics of the Delay Logistic Equation

S. A. Kashchenkoab

a P.G. Demidov Yaroslavl State University
b National Engineering Physics Institute "MEPhI", Moscow

Abstract: The delay logistic equation with rapidly oscillating coefficients is studied. An averaged equation is constructed, and its dynamics is investigated. Algorithms relating the dynamical modes of the original and averaged equations are developed. It is established that the solutions are particularly sensitive to the choice of functions describing the oscillations of the delay coefficient.

Keywords: averaging, stability, normal forms, bifurcations, asymptotics.

DOI: https://doi.org/10.4213/mzm11704

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English version:
Mathematical Notes, 2018, 104:2, 231–243

Bibliographic databases:

UDC: 517.9
PACS: 05.45.-a

Citation: S. A. Kashchenko, “Application of the Averaging Principle to the Study of the Dynamics of the Delay Logistic Equation”, Mat. Zametki, 104:2 (2018), 216–230; Math. Notes, 104:2 (2018), 231–243

Citation in format AMSBIB
\Bibitem{Kas18} \by S.~A.~Kashchenko \paper Application of the Averaging Principle to the Study of the Dynamics of the Delay Logistic Equation \jour Mat. Zametki \yr 2018 \vol 104 \issue 2 \pages 216--230 \mathnet{http://mi.mathnet.ru/mz11704} \crossref{https://doi.org/10.4213/mzm11704} \elib{https://elibrary.ru/item.asp?id=35410183} \transl \jour Math. Notes \yr 2018 \vol 104 \issue 2 \pages 231--243 \crossref{https://doi.org/10.1134/S0001434618070246} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000446511500024} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85054504142} 

• http://mi.mathnet.ru/eng/mz11704
• https://doi.org/10.4213/mzm11704
• http://mi.mathnet.ru/eng/mz/v104/i2/p216

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This publication is cited in the following articles:
1. S. A. Kashchenko, D. O. Loginov, “Andronov–Hopf Bifurcation in Logistic Delay Equations with Diffusion and Rapidly Oscillating Coefficients”, Math. Notes, 108:1 (2020), 50–63
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