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Modelirovanie i Analiz Informatsionnykh Sistem, 2020, Volume 27, Number 3, Pages 344–355
DOI: https://doi.org/10.18255/1818-1015-2020-3-344-355
(Mi mais720)
 

Computer system organization

Features of the algorithmic implementation of difference analogues of the logistic equation with delay

S. D. Glyzin, S. A. Kaschenko, A. O. Tolbey

Centre of Integrable Systems, P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150003, Russia
References:
Abstract: The logistic equation with delay or Hutchinson's equation is one of the fundamental equations of population dynamics and is widely used in problems of mathematical ecology. We consider a family of mappings built for this equation based on central separated differences. Such difference schemes are usually used in the numerical simulation of this problem. The presented mappings themselves can serve as models of population dynamics; therefore, their study is of considerable interest. We compare the properties of the trajectories of these mappings and the original equation with delay. It is shown that the behavior of the solutions of the mappings constructed on the basis of the central separated differences does not preserve, even with a sufficiently small value of the time step, the basic dynamic properties of the logistic equation with delay. In particular, this map does not have a stable invariant curve bifurcating under the oscillatory loss of stability of a nonzero equilibrium state. This curve corresponds in such mappings to the stable limit cycle of the original continuous equation. Thus, it is shown that such a difference scheme cannot be used for numerical modeling of the logistic equation with delay.
Keywords: logistic equation with delay, mapping, bifurcation.
Funding agency Grant number
Russian Foundation for Basic Research 18-29-10043
The author were supported by the Russian Foundation for Basic Research (project no. 18-29-10043).
Received: 11.08.2020
Revised: 07.09.2020
Accepted: 09.09.2020
Document Type: Article
UDC: 517.962.24
MSC: 39A11, 34K18
Language: Russian
Citation: S. D. Glyzin, S. A. Kaschenko, A. O. Tolbey, “Features of the algorithmic implementation of difference analogues of the logistic equation with delay”, Model. Anal. Inform. Sist., 27:3 (2020), 344–355
Citation in format AMSBIB
\Bibitem{GlyKasTol20}
\by S.~D.~Glyzin, S.~A.~Kaschenko, A.~O.~Tolbey
\paper Features of the algorithmic implementation of difference analogues of the logistic equation with delay
\jour Model. Anal. Inform. Sist.
\yr 2020
\vol 27
\issue 3
\pages 344--355
\mathnet{http://mi.mathnet.ru/mais720}
\crossref{https://doi.org/10.18255/1818-1015-2020-3-344-355}
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