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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2023, Volume 513, Pages 51–56
DOI: https://doi.org/10.31857/S2686954323600507 (Mi danma415) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Dynamics of a system of two equations with a large delay

S. A. Kaschenko, A. O. Tolbey

Regional Scientific and Educational Mathematical Center "Centre of Integrable Systems", P.G. Demidov Yaroslavl State University, Yaroslavl, Russian Federation
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DOI: https://doi.org/10.31857/S2686954323600507
Abstract: The local dynamics of systems of two equations with delay is considered. The main assumption is that the delay parameter is large enough. Critical cases in the problem of the stability of the equilibrium state are highlighted and it is shown that they have infinite dimension. Methods of infinite-dimensional normalisation were used and further developed. The main result is the construction of special nonlinear boundary value problems which play the role of normal forms. Their nonlocal dynamics determines the behaviour of all solutions of the original system in а neighbourhood of the equilibrium state.
Keywords: dynamics, stability, delay, quasi-normal forms, singular perturbations.
Funding agency Grant number
Russian Science Foundation 21-71-30011
This work was supported by the Russian Science Foundation, project no. 21-71-30011, https://rscf.ru/en/project/21-71-30011/.
Presented: V. V. Kozlov
Received: 20.06.2023
Revised: 21.07.2023
Accepted: 17.08.2023
English version:
Doklady Mathematics, 2023, Volume 108, Issue 2, Pages 369–373
DOI: https://doi.org/10.1134/S1064562423701259
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: S. A. Kaschenko, A. O. Tolbey, “Dynamics of a system of two equations with a large delay”, Dokl. RAN. Math. Inf. Proc. Upr., 513 (2023), 51–56; Dokl. Math., 108:2 (2023), 369–373
Citation in format AMSBIB
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\by S.~A.~Kaschenko, A.~O.~Tolbey
\paper Dynamics of a system of two equations with a large delay
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2023
\vol 513
\pages 51--56
\mathnet{http://mi.mathnet.ru/danma415}
\crossref{https://doi.org/10.31857/S2686954323600507}
\elib{https://elibrary.ru/item.asp?id=56716530}
\transl
\jour Dokl. Math.
\yr 2023
\vol 108
\issue 2
\pages 369--373
\crossref{https://doi.org/10.1134/S1064562423701259}
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  • https://www.mathnet.ru/eng/danma/v513/p51
    • This publication is cited in the following 1 articles:
    1. Qinghui Liu, Xin Zhang, “Chaos detection in predator-prey dynamics with delayed interactions and Ivlev-type functional response”, MATH, 9:9 (2024), 24555  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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    References:24
     
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