Geodesic
Nonlinear dynamics of the predator - prey system in a heterogeneous habitat and scenarios of local interaction of species
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 29 (2021) no. 5, pp. 751-764.

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The purpose of this work is to study the influence of various local models in the equations of diffusion-advection-reaction on the spatial processes of coexistence of predators and prey under conditions of a nonuniform distribution of the carrying capacity. We consider a system of nonlinear parabolic equations to describe diffusion, taxis, and local interaction of a predator and prey in a one-dimensional habitat. Methods. We carried out the study of the system using the dynamical systems approach and a computational experiment based on the method of lines and a scheme of staggered grids. Results. The behavior of the predator - prey system has been studied for various scenarios of local interaction, taking into account the hyperbolic law of prey growth and the Holling effect with nonuniform carrying capacity. We have established paradoxical scenarios of interaction between prey and predator for several modifications of the trophic function. Stationary and nonstationary solutions are analyzed considering diffusion and directed migration of species. Conclusion. The trophic function that considers the heterogeneity of the resource is proposed, which does not lead to paradoxical dynamics.
Keywords: predator - prey system, nonlinear dynamics, heterogeneous habitat, diffusion, taxis, trophic function. 
@article{IVP_2021_29_5_a4,
     author = {V. G. Tsybulin and D. Ha and P. A. Zelenchuk},
     title = {Nonlinear dynamics of the predator - prey system in a heterogeneous habitat and scenarios of local interaction of species},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {751--764},
     publisher = {mathdoc},
     volume = {29},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2021_29_5_a4/}
}
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V. G. Tsybulin; D. Ha; P. A. Zelenchuk. Nonlinear dynamics of the predator - prey system in a heterogeneous habitat and scenarios of local interaction of species. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 29 (2021) no. 5, pp. 751-764. http://geodesic.mathdoc.fr/item/IVP_2021_29_5_a4/