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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 4, Pages 109–124 (Mi vuu406)  

This article is cited in 5 scientific papers (total in 5 papers)

MATHEMATICS

On some probability models of dynamics of population growth

L. I. Rodina

Department of Mathematical Analysis, Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: The new probability model is developed such that it is applied to the description of dynamics of growth for the isolated population. The conditions of asymptotical degeneration with probability one for the population which development is given by control system with random coefficients are found, and the conditions for the existence of the control leading population to degeneration are obtained, too. We study the dynamic mode of the development for the population which is on the verge of disappearance; it means that with probability one the size of such population will be less than the minimum critical value after which the biological restoration of the population is impossible. The results of the work are illustrated on an example of development of bisexual population.

Keywords: probability models of dynamics of population, probability of degeneration of the population, control systems with random coefficients.

Full text: PDF file (278 kB)
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UDC: 517.935+517.938
MSC: 34A60, 37N35, 49J15, 93B03
Received: 15.10.2013

Citation: L. I. Rodina, “On some probability models of dynamics of population growth”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 4, 109–124

Citation in format AMSBIB
\Bibitem{Rod13}
\by L.~I.~Rodina
\paper On some probability models of dynamics of population growth
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2013
\issue 4
\pages 109--124
\mathnet{http://mi.mathnet.ru/vuu406}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Kh. Khammadi, “Kharakteristiki invariantnosti mnozhestva dostizhimosti upravlyaemykh sistem so sluchainymi koeffitsientami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 2, 100–110  mathnet
    2. L. I. Rodina, “Ob invariantnykh mnozhestvakh upravlyaemykh sistem so sluchainymi koeffitsientami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 4, 109–121  mathnet
    3. L. I. Rodina, I. I. Tyuteev, “Ob asimptoticheskikh svoistvakh reshenii raznostnykh uravnenii so sluchainymi parametrami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:1 (2016), 79–86  mathnet  crossref  mathscinet  elib
    4. L. I. Rodina, “Ob ottalkivayuschikh tsiklakh i khaoticheskikh resheniyakh raznostnykh uravnenii so sluchainymi parametrami”, Tr. IMM UrO RAN, 22, no. 2, 2016, 227–235  mathnet  crossref  mathscinet  elib
    5. L. I. Rodina, “Ob asimptoticheskikh svoistvakh reshenii upravlyaemykh sistem so sluchainymi parametrami”, Vypusk posvyaschen 70-letnemu yubileyu Aleksandra Georgievicha Chentsova, Tr. IMM UrO RAN, 24, no. 1, 2018, 189–199  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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