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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2020, Volume 55, Pages 3–18
DOI: https://doi.org/10.35634/2226-3594-2020-55-01
(Mi iimi387)
 

This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

Influence of random effects on the equilibrium modes in the population dynamics model

E. P. Abramova, T. V. Perevalova

Ural Federal University, pr. Lenina, 51, Yekaterinburg, 620000, Russia
References:
Abstract: In the paper, we study a dynamic model of interacting populations of the type “predator–two prey”. A detailed parametric analysis of the equilibrium modes arising in the system is carried out. In zones of the bifurcation parameter, where the coexistence of several equilibrium regimes is found, separable surfaces are constructed. Those surfaces are the boundaries of the attraction basins of different equilibria. It is shown that the effect of an external random disturbance can destroy the equilibrium mode of coexistence of three populations and lead to a qualitatively different mode of coexistence. Such qualitative changes lead to the extinction of one or two of the three populations. Using the technique of stochastic sensitivity function and the method of confidence domains, the probabilistic mechanisms of destruction of equilibrium modes are demonstrated. A parametric analysis of the probabilities of extinction of populations for two types is carried out. The range of the bifurcation parameter and the level of noise intensity, that are the most favorable for the coexistence of three populations, are discussed.
Keywords: population dynamics, stochastic sensitivity, noise-induced extinction.
Funding agency Grant number
Russian Science Foundation 16-11-10098
This study was supported by the Russian Science Foundation, grant no. 16–11–10098.
Received: 01.02.2020
Bibliographic databases:
Document Type: Article
UDC: 519.21
MSC: 39A50
Language: Russian
Citation: E. P. Abramova, T. V. Perevalova, “Influence of random effects on the equilibrium modes in the population dynamics model”, Izv. IMI UdGU, 55 (2020), 3–18
Citation in format AMSBIB
\Bibitem{AbrPer20}
\by E.~P.~Abramova, T.~V.~Perevalova
\paper Influence of random effects on the equilibrium modes in the population dynamics model
\jour Izv. IMI UdGU
\yr 2020
\vol 55
\pages 3--18
\mathnet{http://mi.mathnet.ru/iimi387}
\crossref{https://doi.org/10.35634/2226-3594-2020-55-01}
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  • This publication is cited in the following 3 articles:
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