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 τk = kd, d > 0, resource shares u(k), k = 0, 1, 2, . . ., are extracted from the population. Regarding \( \overline{\textrm{u}} \) = (u(0), u(1), . . . , u(k), . . . ) as a control for reaching a desired harvesting result, we construct \( \overline{\textrm{u}} \) 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.
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Translated from Problemy Matematicheskogo Analiza 122, 2023, pp. 95-106.
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Rodina, L.I., Chernikova, A.V. Problems of Optimal Resource Harvesting for Infinite Time Horizon. J Math Sci 270, 609–623 (2023). https://doi.org/10.1007/s10958-023-06372-7
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DOI: https://doi.org/10.1007/s10958-023-06372-7