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 Tr. Mat. Inst. Steklova, 2012, Volume 277, Pages 101–143 (Mi tm3379)

Discrete autowaves in systems of delay differential–difference equations in ecology

A. Yu. Kolesova, N. Kh. Rozovb

a Yaroslavl State University, Yaroslavl, Russia
b Moscow State University, Moscow, Russia

Abstract: We propose a theory of relaxation oscillations for a nonlinear scalar delay differential-difference equation that represents a modification of the well-known Hutchinson equation in ecology. In particular, we establish that a one-dimensional chain of diffusively coupled equations of this type exhibits the well-known buffer phenomenon. Namely, under an increase in the number of links in the chain and a consistent decrease in the coupling constant, the number of coexisting stable periodic motions indefinitely increases.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 277, 94–136

Bibliographic databases:

UDC: 517.926

Citation: A. Yu. Kolesov, N. Kh. Rozov, “Discrete autowaves in systems of delay differential–difference equations in ecology”, Mathematical control theory and differential equations, Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko, Tr. Mat. Inst. Steklova, 277, MAIK Nauka/Interperiodica, Moscow, 2012, 101–143; Proc. Steklov Inst. Math., 277 (2012), 94–136

Citation in format AMSBIB
\Bibitem{KolRoz12} \by A.~Yu.~Kolesov, N.~Kh.~Rozov \paper Discrete autowaves in systems of delay differential--difference equations in ecology \inbook Mathematical control theory and differential equations \bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko \serial Tr. Mat. Inst. Steklova \yr 2012 \vol 277 \pages 101--143 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3379} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3052267} \elib{http://elibrary.ru/item.asp?id=17759401} \transl \jour Proc. Steklov Inst. Math. \yr 2012 \vol 277 \pages 94--136 \crossref{https://doi.org/10.1134/S0081543812040086} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000309232900008} \elib{http://elibrary.ru/item.asp?id=23960334} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84904035030} 

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This publication is cited in the following articles:
1. A. Yu. Kolesov, N. Kh. Rozov, V. A. Sadovnichii, “On a Mathematical Model of Biological Self-Organization”, Proc. Steklov Inst. Math., 304 (2019), 160–189
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