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Russia Moscow; Vladimir
Section Mathematics
Title On optimal harvesting of renewable resource from the structured population
Author(-s) Egorova A.V.a, Rodina L.I.ab
Affiliations Vladimir State Universitya, National University of Science and Technology MISISb
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maintained on a finite interval, we describe a craft strategy at which the greatest value of a total cost of a withdrawn resource is reached.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
UDC 517.929
MSC 39A23, 39A99, 49N90, 93C55
DOI 10.20537/vm190403
Received 5 September 2019
Language Russian
Citation Egorova A.V., Rodina L.I. On optimal harvesting of renewable resource from the structured population, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 4, pp. 501-517.
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