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Contemporary Mathematics. Fundamental Directions, 2022, Volume 68, Issue 3, Pages 509–521
DOI: https://doi.org/10.22363/2413-3639-2022-68-3-509-521
(Mi cmfd471)
 

This article is cited in 2 scientific papers (total in 2 papers)

Multistability for a mathematical model of the dynamics of predators and preys in a heterogeneous area

T. D. Haab, V. G. Tsybulina

a Southern Federal University, Rostov-on-Don, Russia
b Vietnam-Hungary Industrial University, Hanoi, Vietnam
Full-text PDF (308 kB) Citations (2)
References:
Abstract: We consider the system of reaction–diffusion–advection equations describing the evolution of the spatial distributions of two populations of predators and two prey populations. This model allows us to consider directed migration, the Holling functional response of the second kind, and the hyperbolic prey growth function. We obtain conditions on the parameters under which cosymmetries exist. As a result, multistability is realized, i.e., the one- and two-parameter families of stationary solutions appear. For a homogeneous environment, we analytically derive explicit formulas for equilibria. With a heterogeneous habitat, we computed distributions of species using the method of lines and the scheme of staggered grids. We present the results of violation of cosymmetry and transformation of the family in the case of invasion of a predator.
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: T. D. Ha, V. G. Tsybulin, “Multistability for a mathematical model of the dynamics of predators and preys in a heterogeneous area”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 68, no. 3, PFUR, M., 2022, 509–521
Citation in format AMSBIB
\Bibitem{HaTsy22}
\by T.~D.~Ha, V.~G.~Tsybulin
\paper Multistability for a mathematical model of the dynamics of predators and preys in a heterogeneous area
\inbook Proceedings of the Crimean autumn mathematical school-symposium
\serial CMFD
\yr 2022
\vol 68
\issue 3
\pages 509--521
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd471}
\crossref{https://doi.org/10.22363/2413-3639-2022-68-3-509-521}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4497488}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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