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maintained on a finite interval, we describe a craft strategy at which the greatest value of a total cost of a withdrawn resource is reached.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.
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
\Bibitem{CheRod19}
\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}
Linking options:
https://www.mathnet.ru/eng/vuu697
https://www.mathnet.ru/eng/vuu/v29/i4/p501
This publication is cited in the following 8 articles:
L. I. Rodina, A. V. Chernikova, “Ob optimalnoi dobyche vozobnovlyaemogo resursa na beskonechnom promezhutke vremeni”, Tr. IMM UrO RAN, 29, no. 1, 2023, 167–179
A. A. Bazulkina, “Otsenka summarnogo dokhoda s uchetom diskontirovaniya dlya veroyatnostnykh modelei dinamiki populyatsii”, Vestnik rossiiskikh universitetov. Matematika, 28:143 (2023), 217–226
L. I. Rodina, A. V. Chernikova, “Problems of Optimal Resource Harvesting for Infinite Time Horizon”, J Math Sci, 270:4 (2023), 609
M. S. Woldeab, L. I. Rodina, “About the methods of biological resourse extraction, that provide the maximum average time benefit”, Russian Math. (Iz. VUZ), 66:1 (2022), 8–18
M. S. Voldeab, L. I. Rodina, “O sposobakh dobychi vozobnovlyaemogo resursa iz strukturirovannoi populyatsii”, Vestnik rossiiskikh universitetov. Matematika, 27:137 (2022), 16–26
A. A. Rodin, L. I. Rodina, A. V. Chernikova, “O sposobakh ekspluatatsii populyatsii, zadannoi raznostnym uravneniem so sluchainymi parametrami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:2 (2022), 211–227
A. V. Chernikova, “O suschestvovanii predela srednei vremennoi vygody v veroyatnostnykh modelyakh sbora vozobnovlyaemogo resursa”, Vestnik rossiiskikh universitetov. Matematika, 27:140 (2022), 386–404
A. V. Egorova, “Optimizatsiya diskontirovannogo dokhoda dlya strukturirovannoi populyatsii, podverzhennoi promyslu”, Vestnik rossiiskikh universitetov. Matematika, 26:133 (2021), 15–25
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