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
\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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https://www.mathnet.ru/eng/cmfd471
https://www.mathnet.ru/eng/cmfd/v68/i3/p509
This publication is cited in the following 2 articles:
P. A. Zelenchuk, V. G. Tsibulin, “Matematicheskaya model idealnogo svobodnogo raspredeleniya v sisteme khischnik—zhertva”, SMFN, 69, no. 2, Rossiiskii universitet druzhby narodov, M., 2023, 237–249
B. Kh. Nguen, V. G. Tsibulin, “Matematicheskaya model trekh konkuriruyuschikh populyatsii i multistabilnost periodicheskikh rezhimov”, Izvestiya vuzov. PND, 31:3 (2023), 316–333
Citation in format AMSBIB
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