Section
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Mathematics
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Title
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On optimal harvesting of renewable resource from the structured population
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Author(-s)
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Egorova A.V.a,
Rodina L.I.ab
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Affiliations
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Vladimir State Universitya,
National University of Science and Technology MISISb
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Abstract
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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maintained on a finite interval, we describe a craft strategy at which the greatest value of a total cost of a withdrawn resource is reached.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.
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Keywords
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model of the population subject to harvesting, average time profit, optimal exploitation, modes of exploitation of the population
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UDC
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517.929
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MSC
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39A23, 39A99, 49N90, 93C55
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DOI
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10.20537/vm190403
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Received
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5 September 2019
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Language
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Russian
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Citation
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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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References
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- Leslie P.H. On the use of matrices in certain population mathematics, Biometrika, 1945, vol. 33, issue 3, pp. 183-212. https://doi.org/10.1093/biomet/33.3.183
- Logofet D.O., Belova I.N. Nonnegative matrices as a tool to model population dynamics: classical models and contemporary expansions, Journal of Mathematical Sciences, 2008, vol. 155, no. 6, pp. 894-907. https://doi.org/10.1007/s10958-008-9249-2
- Neverova G.P., Abakumov A.I., Frisman E.Ya. Dynamic modes of exploited limited population: results of modeling and numerical study, Math. Biol. Bioinf., 2016, vol. 11, issue 1, pp. 1-13 (in Russian). https://doi.org/10.17537/2016.11.1
- Revutskaya O.L., Frisman E.Ya. Influence of stationary harvesting on development of a two-age population scenario, Informatika i Sistemy Upravleniya, 2017, no. 3 (53), pp. 36-48 (in Russian). https://doi.org/10.22250/isu.2017.53.36-48
- Ashikhmina E.V., Izrailsky Yu.G. Harvest optimization for population, when environment conditions limiting population growth change cyclically, Informatika i Sistemy Upravleniya, 2009, no. 2, pp. 11-18 (in Russian). https://elibrary.ru/item.asp?id=12511358
- Neverova G.P., Abakumov A.I., Frisman E.Ya. Dynamic modes of limited structured population under age specific harvest, Math. Biol. Bioinf., 2017, vol. 12, issue 2, pp. 327-342 (in Russian). https://doi.org/10.17537/2017.12.327
- Belyakov A.O., Davydov A.A. Efficiency optimization for the cyclic use of a renewable resource, Proceedings of the Steklov Institute of Mathematics, 2017, vol. 299, suppl. 1, pp. 14-21. https://doi.org/10.1134/S0081543817090036
- Zelikin M.I., Lokutsievskiy L.V., Skopincev S.V. On optimal harvesting of a resource on a circle, Mathematical Notes, 2017, vol. 102, no. 4, pp. 521-532. https://doi.org/10.1134/S0001434617090243
- Belyakov A.O., Veliov V.M. On optimal harvesting in age-structured populations, Dynamic Perspectives on Managerial Decision Making, 2016, pp. 149-166. https://doi.org/10.1007/978-3-319-39120-5_9
- Frisman E.Ya., Kulakov M.P., Revutskaya O.L., Zhdanova O.L., Neverova G.P.The key approaches and review of current researches on dynamics of structured and interacting populations, Computer Research and Modeling, 2019, vol. 11, issue 1, pp. 119-151 (in Russian). https://doi.org/10.20537/2076-7633-2019-11-1-119-151
- Rodina L.I. Optimization of average time profit for a probability model of the population subject to a craft, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 1, pp. 48-58 (in Russian). https://doi.org/10.20537/vm180105
- Rodina L.I. Properties of average time prot in stochastic models of harvesting a renewable resource, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 2, pp. 213-221 (in Russian). https://doi.org/10.20537/vm180207
- Svirezhev Yu.M., Logofet D.O. Ustoichivost' biologicheskikh soobshchestv (Stability of biological communities), Moscow: Nauka, 1978.
- Sharkovskii A.N., Kolyada S.F., Sivak A.G., Fedorenko V.V. Dinamika odnomernykh otobrazhenii (Dynamics of one-dimensional mappings), Kiev: Naukova dumka, 1989, 216 p.
- Frisman E.Ya., Sycheva E.V., Izrailsky Yu.G. The mathematical model of the number dynamic for the homogeneous exploited population and analysis of the trade influence on the dynamic character, Dal'nevost. Mat. Zh. 2002, vol. 3, no. 1, pp. 108-122 (in Russian). http://mi.mathnet.ru/eng/dvmg122
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