Analysis the model of co-existing of species, which competing on spatially inhomogeneous area

Authors

  • Kruglikov M.G. Southern Federal University, Rostov-on-Don, Российская Федерация
  • Tsybulin V.G. Southern Federal University, Rostov-on-Don, Российская Федерация

UDC

519.63

Abstract

Modeling of population dynamics on the inhomogeneous area is based on a system of nonlinear parabolic equations with variable coefficients. We apply the theory cosymmetry to analyze different scenario of coexistence of populations consuming a single resource. Appearence of a continuous family of steady states is found under the some conditions on the parameters of diffusion and growth. Theoretical analysis is justified by computer simulations based on the method of lines and staggered grids scheme. The case of two populations on the one-dimensional habitat (ring) is studied numerically. It was found that after destruction of cosymmetry the family of steady states may transform to a stable configuration of coexisting species. The corresponding maps of growth parameters are presented.

Keywords:

population dynamics, nonlinear parabolic equations, cosymmetry, carrying capacity, method of lines

Acknowledgement

Исследование проводилось при финансовой поддержке РФФИ (14-01-00470).

Author Infos

Mikhail G. Kruglikov

аспирант кафедры вычислительной математики и математической физики Южного федерального университета

e-mail: kruglicov@gmail.com

Vyacheslav G. Tsybulin

д-р физ.-мат. наук, профессор кафедры кафедры вычислительной математики и математической физики Южного федерального университета

e-mail: vtsybulin04@gmail.com

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Issue

2015. No. 2

Pages

56-64

Submitted

2015-05-22

Published

2015-06-25

How to Cite

Kruglikov M.G., Tsybulin V.G. Analysis the model of co-existing of species, which competing on spatially inhomogeneous area. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2015, no. 2, pp. 56-64. (In Russian)

Copyright (c) 2015 Kruglikov M.G., Tsybulin V.G.

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