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 Model. Anal. Inform. Sist., 2017, Volume 24, Number 2, Pages 168–185 (Mi mais556)

About bifurcations at small perturbations in a logistic equation with delay

S. A. Kashchenko

P.G. Demidov Yaroslavl State University, 14 Sovetskaya str., Yaroslavl 150003, Russia

Abstract: The article considers bifurcation problems for a logistic equation with delay at small perturbations. The most interesting results are for the case when small perturbations contain a large delay. The main results are special nonlinear equations of evolution in the normal form. Their nonlocal dynamics defines the behaviour of the solutions of the original equation in a small neigbourhood of the balance state or the cycle. It turns out that the order of large delay magnitude is principal. For the simplest case, when this order is congruent with the magnitude inverse to the small parameter appearing in the equation, the normal form is a complex equation with delay. In the case when the order of the delay coefficient is even higher, the normal form is presented by a multiparameter family of special boundary-value problems of degenerate-parabolic type. All these things allow to make a conclusion about the fact that in the considered problems with large delay the multistability is typical.

Keywords: nonlinear dynamics, bifurcation, asymptotic presentation.

DOI: https://doi.org/10.18255/1818-1015-2017-2-168-185

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UDC: 517.9

Citation: S. A. Kashchenko, “About bifurcations at small perturbations in a logistic equation with delay”, Model. Anal. Inform. Sist., 24:2 (2017), 168–185

Citation in format AMSBIB
\Bibitem{Kas17} \by S.~A.~Kashchenko \paper About bifurcations at small perturbations in a logistic equation with delay \jour Model. Anal. Inform. Sist. \yr 2017 \vol 24 \issue 2 \pages 168--185 \mathnet{http://mi.mathnet.ru/mais556} \crossref{https://doi.org/10.18255/1818-1015-2017-2-168-185} \elib{http://elibrary.ru/item.asp?id=29064000} 

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This publication is cited in the following articles:
1. S. A. Kaschenko, “Usrednenie po prostranstvennoi peremennoi v nelineinykh parabolicheskikh sistemakh”, Tr. MMO, 80, no. 1, MTsNMO, M., 2019, 63–86
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