Archive of Issues
Russia Izhevsk
Section  Mathematics 
Title  On some probability models of dynamics of population growth 
Author(s)  Rodina L.I.^{a} 
Affiliations  Udmurt State University^{a} 
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 
UDC  517.935, 517.938 
MSC  34A60, 37N35, 49J15, 93B03 
DOI  10.20537/vm130411 
Received  15 October 2013 
Language  Russian 
Citation  Rodina L.I. On some probability models of dynamics of population growth, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 4, pp. 109124. 
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