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Russian Mathematical Surveys, 2012, Volume 67, Issue 2, Pages 297–343
DOI: https://doi.org/10.1070/RM2012v067n02ABEH004788 (Mi rm9469) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Self-excited wave processes in chains of diffusion-linked delay equations

A. Yu. Kolesova, N. Kh. Rozovb

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University
English version PDF (818 kB) Citations (7) Russian version article
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DOI: https://doi.org/10.1070/RM2012v067n02ABEH004788
Abstract: A new mathematical object is introduced, a scalar non-linear difference-differential equation with time delay which is a certain modification of the Hutchinson equation well-known in ecology. It is shown that the buffering phenomenon occurs in a one-dimensional chain of diffusion-linked equations of this type. Namely, as the number of links grows in a way compatible with a decrease of the diffusion coefficient, the number of co-existing stable periodic solutions of the system increases without limit.
Bibliography: 15 titles.
Keywords: modified Hutchinson equation, self-excited wave processes, relaxation cycle, asymptotic behaviour, stability.
Received: 14.06.2011
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, “Self-excited wave processes in chains of diffusion-linked delay equations”, Russian Math. Surveys, 67:2 (2012), 297–343
Citation in format AMSBIB
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\by A.~Yu.~Kolesov, N.~Kh.~Rozov
\paper Self-excited wave processes in chains of diffusion-linked delay equations
\jour Russian Math. Surveys
\yr 2012
\vol 67
\issue 2
\pages 297--343
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  • https://doi.org/10.1070/RM2012v067n02ABEH004788
  • https://www.mathnet.ru/eng/rm/v67/i2/p109
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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