Geodesic
Multistability for a mathematical model of the dynamics of predators and preys in a heterogeneous area
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 68 (2022) no. 3, pp. 509-521

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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. 
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     author = {T. D. Ha and V. G. Tsybulin},
     title = {Multistability for a mathematical model of the dynamics of predators and preys in a heterogeneous area},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2022_68_3_a6/}
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T. D. Ha; V. G. Tsybulin. Multistability for a mathematical model of the dynamics of predators and preys in a heterogeneous area. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 68 (2022) no. 3, pp. 509-521. http://geodesic.mathdoc.fr/item/CMFD_2022_68_3_a6/