|
Section
|
Mathematics
|
|
Title
|
On some probability models of dynamics of population growth
|
|
Author(-s)
|
Rodina L.I.a
|
|
Affiliations
|
Udmurt State Universitya
|
|
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. 109-124.
|
|
References
|
- Nedorezov L.V. Kurs lektsii po matematicheskoi ekologii (Course of lectures on mathematical ecology), Novosibirsk: Sibirskii khronograf, 1997, 161 p.
- Nedorezov L.V., Utyupin Yu.V. A discrete-continuous model for a bisexual population dynamics, Sibirskii Matematicheskii Zhurnal, 2003, vol. 44, no. 3, pp. 650-659.
- Kasсhenko S.A. Stationary states of a delay differentional equation of insect population's dynamics, Modelirovanie i Analiz Informatsionnykh Sistem, 2012, vol. 19, no. 5, pp. 18-34.
- Nagaev S.V., Nedorezov L.V., Vakhtel' V.I. A probabilistic continuous-discrete model of the dynamics of the size of an isolated population, Sibirskii Zhurnal Industrial'noi Matematiki, 1999, vol. 2, no. 2 (4), pp. 147-152.
- Kolmogorov A.N. Qualitative study of mathematical models of population dynamics, Problemy Kibernetiki, issue 25, Moscow: Nauka, 1972, pp. 101-106.
- Kornfel'd I.P., Sinai Ya.G., Fomin S.V. Ergodicheskaya teoria (The ergodic theory), Moscow: Nauka, 1980, 384 p.
- Rodina L.I. Invariant and statistically weakly invariant sets of control systems, Izv. Inst. Mat. Inform. Udmurt. Gos. Univ., 2012, no. 2 (40), pp. 3-164.
- Shiryaev A.N. Veroyatnost' (Probability), Moscow: Nauka, 1989, 580 p.
- Korolyuk V.S., Portenko N.I., Skorokhod A.V., Turbin A.F. Spravochnik po teorii veroyatnostei I matematicheskoi statistike (Handbook of probability theory and mathematical statistics), Moscow: Nauka, 1985, 640 p.
- Feller W. An introduction to probability theory and its applications, Wiley, 1971. Translated under the title Vvedenie v teoriyu veroyatnostei i ee prilozheniya, vol. 1, Moscow: Mir, 1984, 529 p.
- Kuzenkov O.A., Ryabova E.A. Matematicheskoe modelirovanie protsessov otbora (Mathematical modeling of processes of selection), Nizhnii Novgorod: Nizhnii Novgorod State University, 2007, 324 p.
- Demidovich B.P. Lektsii po matematicheskoi teorii ustoichivosti (Lectures on the mathematical theory of stability), Moscow: Nauka, 1967, 472 p.
- Clarke F. Optimization and nonsmooth analysis, Wiley, 1983. Translated under the title Optimizatsiya i negladkii analiz, Moscow: Nauka, 1988, 300 p.
- Panasenko E.A., Tonkov E.L. Invariant and stably invariant sets for differential inclusions, Proceedings of the Steklov Institute of Mathematics, 2008, vol. 262, issue 1, pp. 194-212.
- Blagodatskikh V.I., Filippov A.F. Differential inclusions and optimal control, Trudy Mat. Inst. Steklov, 1985, vol. 169, pp. 194-252.
- Rodina L.I., Tonkov E.L. Statistical characteristics of attainable set of controllable system, non-wandering, and minimal attraction center, Nelineinaya Dinamika, 2009, vol. 5, no. 2, pp. 265-288.
|
|
Full text
|
|
+7 (3412) 91 60 92
Russian