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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 5, Pages 766–778
DOI: https://doi.org/10.7868/S0044466914050123 (Mi zvmmf10031) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Dynamics of the logistic delay equation with a large spatially distributed control coefficient

I. S. Kashchenkoa, S. A. Kashchenkob

a Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia
b National Research Nuclear University “MEPhI”, Kashirskoe sh. 31, Moscow, 115409, Russia
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DOI: https://doi.org/10.7868/S0044466914050123
Abstract: The local dynamics of the logistic delay equation with a large spatially distributed control coefficient is asymptotically studied. The basic bifurcation scenarios are analyzed depending on the relations between the parameters of the equation. It is shown that the equilibrium states can lose stability even for asymptotically small values of the delay parameter. The corresponding critical cases can have an infinite dimension. Special nonlinear parabolic equations are constructed whose nonlocal dynamics determine the local behavior of solutions to the original boundary value problem.
Key words: dynamics of the logistic delay equation, spatially distributed control, bifurcation, asymptotic methods, parabolic equations.
Received: 18.11.2013
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 5, Pages 785–796
DOI: https://doi.org/10.1134/S0965542514050108
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: I. S. Kashchenko, S. A. Kashchenko, “Dynamics of the logistic delay equation with a large spatially distributed control coefficient”, Zh. Vychisl. Mat. Mat. Fiz., 54:5 (2014), 766–778; Comput. Math. Math. Phys., 54:5 (2014), 785–796
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  • https://www.mathnet.ru/eng/zvmmf/v54/i5/p766
    • This publication is cited in the following 3 articles:
    1. N. T. Levashova, N. A. Mikheev, “Cauchy Problem for a Singularly Perturbed Delay Equation”, VMU, 2023, no. №5_2023, 2350103–1  crossref
    2. N. T. Levashova, N. A. Mikheev, “Cauchy Problem for a Singularly Perturbed Delay Equation”, Moscow Univ. Phys., 78:5 (2023), 595  crossref
    3. T. Sh. Morgoshia, S. S. Mosoyan, “The application of the operation according to the method Billroth-I in cancer patients: past and present”, Bulletin of the Russian Military Medical Academy, 19:2 (2017), 245  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    Full-text PDF :75
    References:91
    First page:22
     
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