Problems of Optimal Resource Harvesting for Infinite Time Horizon

We consider a population such that, in absence of exploitation, its dynamics is described by a system of differential equations. It is assumed that, at certain times τ k = kd, d > 0, resource shares u(k), k = 0, 1, 2, . . ., are extracted from the population. Regarding u ¯ = (u(0), u(1), . . . ,...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 270; no. 4; pp. 609 - 623
Main Authors Rodina, L. I., Chernikova, A. V.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2023
Springer
Springer Nature B.V
Subjects
Differential equations
Harvesting
Mathematics
Mathematics and Statistics
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Summary:We consider a population such that, in absence of exploitation, its dynamics is described by a system of differential equations. It is assumed that, at certain times τ k = kd, d > 0, resource shares u(k), k = 0, 1, 2, . . ., are extracted from the population. Regarding u ¯ = (u(0), u(1), . . . , u(k), . . . ) as a control for reaching a desired harvesting result, we construct u ¯ at which the resource harvesting characteristics (the time-average harvesting profit and the harvesting efficiency) attain given values, in particular, the case where the harvesting efficiency becomes infinite is included. We consider the problems of constructing stationary controls delivering the maximum value for one of the characteristics provided that the other is fixed and demonstrate the solution of these problems by considering examples of homogeneous and two-species populations.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06372-7