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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.

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

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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  
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  
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        
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        
5. L. I. Rodina, “On asymptotic properties of solutions of control systems with random parameters”, Proc. Steklov Inst. Math. (Suppl.), 304, suppl. 1 (2019), S144–S153          

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles