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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, Volume 27, Number 2, Pages 99–107
DOI: https://doi.org/10.21538/0134-4889-2021-27-2-99-107 (Mi timm1817) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Optimal states of distributed exploited populations with periodic impulse selection

A. A. Davydovab, D. A. Melnika

a Lomonosov Moscow State University
b National University of Science and Technology «MISIS», Moscow
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DOI: https://doi.org/10.21538/0134-4889-2021-27-2-99-107
Abstract: The dynamics of a population distributed on a torus is described by an equation of the Kolmogorov–Petrovsky–Piskunov–Fisher type in the divergence form. The population is exploited by periodic sampling of a constant distributed measurable ratio of its density. We prove that there exists a sampling ratio maximizing the time-averaged income in kind, i.e., a ratio that provides an optimal stationary exploitation in the long run.
Keywords: distributed population, Kolmogorov–Petrovsky–Piskunov–Fisher equation, impulse control, optimal solution.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0718-2020-0025
Russian Science Foundation 19-11-00223
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (the first author, results on the properties of the quality functional, project no. 0718-2020-0025) and by the Russian Science Foundation (both authors, main theorem, project no. 19-11-00223).
Received: 30.03.2021
Revised: 12.04.2021
Accepted: 19.04.2021
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2021, Volume 315, Issue 1, Pages S81–S88
DOI: https://doi.org/10.1134/S0081543821060079
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 49J15
Language: Russian
Citation: A. A. Davydov, D. A. Melnik, “Optimal states of distributed exploited populations with periodic impulse selection”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 2, 2021, 99–107; Proc. Steklov Inst. Math. (Suppl.), 315, suppl. 1 (2021), S81–S88
Citation in format AMSBIB
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\paper Optimal states of distributed exploited populations with periodic impulse selection
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\issue 2
\pages 99--107
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\jour Proc. Steklov Inst. Math. (Suppl.)
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