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Sbornik: Mathematics, 2011, Volume 202, Issue 6, Pages 829–858
DOI: https://doi.org/10.1070/SM2011v202n06ABEH004168 (Mi sm7653) 		 
This article is cited in 13 scientific papers (total in 13 papers)

The theory of relaxation oscillations for Hutchinson's equation

A. Yu. Kolesova, N. Kh. Rozovb

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (460 kB) Citations (13) Russian version article
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DOI: https://doi.org/10.1070/SM2011v202n06ABEH004168
Abstract: Hutchinson's equation is a scalar equation with time delay which is well known in ecology. In this paper a complete asymptotic representation is constructed for a stable relaxation cycle of this equation, in the form of series in integer powers of a certain small parameter. The techniques of asymptotic integration developed on the way are then applied to analyse the question of attractors for a system of circularly interrelated Hutchinson equations.
Bibliography: 8 titles.
Keywords: delay system, relaxation oscillations, asymptotic behaviour, stability.
Received: 17.11.2009 and 18.06.2010
Bibliographic databases:
Document Type: Article
UDC: 517.926
MSC: Primary 34C26, 92D40; Secondary 34D45, 37N25
Language: English
Original paper language: Russian
Citation: A. Yu. Kolesov, N. Kh. Rozov, “The theory of relaxation oscillations for Hutchinson's equation”, Sb. Math., 202:6 (2011), 829–858
Citation in format AMSBIB
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\by A.~Yu.~Kolesov, N.~Kh.~Rozov
\paper The theory of relaxation oscillations for Hutchinson's equation
\jour Sb. Math.
\yr 2011
\vol 202
\issue 6
\pages 829--858
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  • https://www.mathnet.ru/eng/sm/v202/i6/p51
    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:833
    Russian version PDF:235
    English version PDF:39
    References:75
    First page:33
     
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