The ideal free distribution in a "predator-prey" model with Holling type II functional response

Authors

  • Zelenchuk P.A. South Federal University, Bol'shaya Sadovaya str., 105/42, Rostov-on-Don, 344006, Russia, Russian Federation ORCID 0000-0001-6598-8521

UDC

519.63

DOI:

https://doi.org/10.31429/vestnik-19-1-6-15

Abstract

This work describes the predator-prey system in the heterogeneous ring habitat. The model is based on reaction-diffusion-advection equations with Holling functional response type II. The heterogeneity of the habitat is determined by the function of prey resource. The system equations model multifactor taxis of both species, taking into account various laws of prey growth. Stationary solution for two coexisting species corresponding to the Ideal Free Distribution (IFD) is analyzed. The boundaries of the stability of this solution are found. Relations between diffusion and taxis coefficients are established at which the IFD is realized. The behavior of the predator-prey system has been studied for various values of the Holling coefficient and power n in the prey’s growth function. Numerical analysis of equations based on the finite difference method and shifted grids is implemented in MATLAB software. Transformations of the IFD at the stationary solution due to small parameters deviation are studied.

Keywords:

population dynamics, Ideal Free Distribution, predator-prey model, reaction-diffusion-advection equation, Holling type II functional response, heterogeneous habitat

Author Info

Pavel A. Zelenchuk

ассистент кафедры теоретической и компьютерной гидроаэродинамики института математики, механики и компьютерных наук им. И.И. Воровича Южного федерального университета

e-mail: zelenchukpavel@mail.ru

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Issue

2022. Vol. 19. No. 1

Section

Mathematics

Pages

6-15

Submitted

2022-02-09

Published

2022-03-30

How to Cite

Zelenchuk P.A. The ideal free distribution in a "predator-prey" model with Holling type II functional response. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2022, vol. 19, no. 1, pp. 6-15. DOI: https://doi.org/10.31429/vestnik-19-1-6-15 (In Russian)

Copyright (c) 2022 Zelenchuk P.A.

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