Abstract:
This article discusses a family of maps that are used in the numerical simulation of a logistic equation with delay. This equation is widely used in problems of mathematical ecology. At the same time, the presented maps themselves can serve as models of the dynamics of populations; therefore, their study is of considerable interest. The paper compares the properties of the trajectories of these mappings and the original equation with delay. It is shown that the behavior of the solutions of maps can be quite complicated, while the logistic equation with delay has only a stable equilibrium state or cycle.
Keywords:
logistic equation with delay, maps, bifurcations.
Citation:
S. D. Glyzin, S. A. Kashchenko, “Family of finite-dimensional maps induced by a logistic equation with a delay”, Mat. Model., 32:3 (2020), 19–46; Math. Models Comput. Simul., 12:6 (2020), 856–873
\Bibitem{GlyKas20}
\by S.~D.~Glyzin, S.~A.~Kashchenko
\paper Family of finite-dimensional maps induced by a logistic equation with a delay
\jour Mat. Model.
\yr 2020
\vol 32
\issue 3
\pages 19--46
\mathnet{http://mi.mathnet.ru/mm4161}
\crossref{https://doi.org/10.20948/mm-2020-03-02}
\transl
\jour Math. Models Comput. Simul.
\yr 2020
\vol 12
\issue 6
\pages 856--873
\crossref{https://doi.org/10.1134/S2070048220060101}
Linking options:
https://www.mathnet.ru/eng/mm4161
https://www.mathnet.ru/eng/mm/v32/i3/p19
This publication is cited in the following 2 articles:
S. D. Glyzin, S. A. Kashchenko, A. O. Tolbey, “Features of the algorithmic implementation of difference analogs of the delayed logistic equation”, Autom. Control Comp. Sci., 55:7 (2021), 723–730
S. D. Glyzin, S. A. Kaschenko, A. O. Tolbei, “Osobennosti algoritmicheskoi realizatsii raznostnykh analogov logisticheskogo uravneniya s zapazdyvaniem”, Model. i analiz inform. sistem, 27:3 (2020), 344–355
Citation in format AMSBIB
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