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Sibirskii Zhurnal Industrial'noi Matematiki, 2011, Volume 14, Number 2, Pages 84–94 (Mi sjim670)  

This article is cited in 1 scientific paper (total in 1 paper)

Statistical modeling of the dynamics of populations affected by toxic pollutants

N. V. Pertsev, B. Yu. Pichugin, K. K. Loginov

Omsk Branch, Sobolev Institute of Mathematics SB RAS, Omsk, RUSSIA
Full-text PDF (349 kB) Citations (1)
References:
Abstract: We present a stochastic model describing the dynamics of competing populations whose individua are affected by toxic pollutants. In order to construct the model, we use a probabilistic analog of the Lotka–Volterra model as a multidimensional inhomogeneous nonlinear birth and death process. We complement the postulates of the birth and death process with a description of the mechanism how? the toxic substance affects the death rate. We construct recurrences describing the dynamics of the population and the quantity of the toxic substance in the environment. We develop an algorithm for modeling the dynamics of populations and the quantity of the toxic substance basing on the Monte-Carlo method. We present the results of simulations studying degeneration conditions for one of the two competing populations, as well as conditions which guarantee that their numbers are maintained at nonzero stationary levels. In order to study analytically the behavior of the expected values of the populations we construct an auxiliary model as a system of nonlinear differential equations.
Received: 03.06.2010
Bibliographic databases:
Document Type: Article
UDC: 519.245+57.022
Language: Russian
Citation: N. V. Pertsev, B. Yu. Pichugin, K. K. Loginov, “Statistical modeling of the dynamics of populations affected by toxic pollutants”, Sib. Zh. Ind. Mat., 14:2 (2011), 84–94
Citation in format AMSBIB
\Bibitem{PerPicLog11}
\by N.~V.~Pertsev, B.~Yu.~Pichugin, K.~K.~Loginov
\paper Statistical modeling of the dynamics of populations affected by toxic pollutants
\jour Sib. Zh. Ind. Mat.
\yr 2011
\vol 14
\issue 2
\pages 84--94
\mathnet{http://mi.mathnet.ru/sjim670}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2962158}
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  • https://www.mathnet.ru/eng/sjim670
  • https://www.mathnet.ru/eng/sjim/v14/i2/p84
  • This publication is cited in the following 1 articles:
    1. N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Stochastic modeling of local by time and location contacts of individuals in the epidemic process”, J. Appl. Industr. Math., 17:2 (2023), 355–369  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский журнал индустриальной математики
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    References:67
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