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 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2019, Volume 29, Issue 4, Pages 501–517 (Mi vuu697)

MATHEMATICS

On optimal harvesting of renewable resource from the structured population

A. V. Egorovaa, L. I. Rodinaba

b Department of Mathematics, National University of Science and Technology MISIS, Leninskii pr., 4, Moscow, 119049, Russia

Abstract: We consider the structured population which individuals are divided into age or typical groups, set by the normal independent system of difference equations. For the given population the problem of optimum harvesting of a renewed resource on finite or infinite time intervals is investigated. For the population maintained on a finite interval, we describe a craft strategy at which the greatest value of a total cost of a withdrawn resource is reached. If resource extraction occurs on an unlimited interval, we define average time profit and calculate its value at a stationary mode of operation; cases when the system has an asymptotically steady motionless point or a steady cycle are considered. A craft strategy which is optimum among other ways of operation is also described; it is shown, that under certain conditions it is stationary or differs from stationary only in value of control during the initial moment of time. The results of work are illustrated by an example of two-age exploited population in which individuals of either younger or both age groups are subject to trade.

Keywords: model of the population subject to harvesting, average time profit, optimal exploitation, modes of exploitation of the population.

DOI: https://doi.org/10.20537/vm190403

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Full text: http://vm.udsu.ru/.../2019-4-3
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Bibliographic databases:

UDC: 517.929
MSC: 39A23, 39A99, 49N90, 93C55

Citation: A. V. Egorova, L. I. Rodina, “On optimal harvesting of renewable resource from the structured population”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:4 (2019), 501–517

Citation in format AMSBIB
\Bibitem{EgoRod19} \by A.~V.~Egorova, L.~I.~Rodina \paper On optimal harvesting of renewable resource from the structured population \jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki \yr 2019 \vol 29 \issue 4 \pages 501--517 \mathnet{http://mi.mathnet.ru/vuu697} \crossref{https://doi.org/10.20537/vm190403}