Optimal control problem of a discrete spatiotemporal prey-predator three-species fishery model

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dc.citation.epage538
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та обчислення
dc.citation.spage528
dc.citation.volume11
dc.contributor.affiliationУніверситет Хасана ІІ Касабланки
dc.contributor.affiliationHassan II University of Casablanca
dc.contributor.authorСаккум, А.
dc.contributor.authorТуфга, Х.
dc.contributor.authorХізазі, Х.
dc.contributor.authorЛхаус, М.
dc.contributor.authorМагрі, Е. М.
dc.contributor.authorSakkoum, A.
dc.contributor.authorToufga, H.
dc.contributor.authorHizazi, H.
dc.contributor.authorLhous, M.
dc.contributor.authorMagri, E. M.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-10-20T08:10:24Z
dc.date.created2024-02-27
dc.date.issued2024-02-27
dc.description.abstractУцій статті обговорюємо просторово-часову дискретну модель “хижака–жертва”. Вона складається з трьох складових: здобич, хижак і суперхижак. Запропонована модель описує взаємодію між жертвою, хижаком і суперхижаком в області з дискретним переміщенням. Також проводиться дослідження відповідних регіональних стратегій керування. Елементи керування застосовуються відповідно до хижака та суперхижака; вони представляють вилов їх у виміряних кількостях у вибраному просторі та часі. Мета збільшити кількість здобичі та зменшити чисельність хижаків, відновити систему харчового ланцюга та забезпечити її стійкість. Накінець, подано графічну візуалізацію та чисельне моделювання для підтвердження наших аналітичних висновкiв.
dc.description.abstractIn this work, we discuss a spatiotemporal discrete prey–predator model. It consists of three compartments: prey, predator, and super-predator. The proposed model describes the interaction between prey, predator, and super-predator in a region with a discrete displacement. We also provide research on appropriate regional control strategies. The controls are applied to the predator and the super-predator, respectively; they represent catching these in measured quantities in a space and a time chosen. The aim is to increase the number of prey and reduce the number of predators, restore the food chain system, and ensure its sustainability. Finally, we provide graphical visuals and numerical simulations to support our analytical findings.
dc.format.extent528-538
dc.format.pages11
dc.identifier.citationOptimal control problem of a discrete spatiotemporal prey-predator three-species fishery model / A. Sakkoum, H. Toufga, H. Hizazi, M. Lhous, E. M. Magri // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 2. — P. 528–538.
dc.identifier.citationenOptimal control problem of a discrete spatiotemporal prey-predator three-species fishery model / A. Sakkoum, H. Toufga, H. Hizazi, M. Lhous, E. M. Magri // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 11. — No 2. — P. 528–538.
dc.identifier.doidoi.org/10.23939/mmc2024.02.528
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/113813
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та обчислення, 2 (11), 2024
dc.relation.ispartofMathematical Modeling and Computing, 2 (11), 2024
dc.relation.references[1] Hui L. Pollution, overfishing destroy East China Sea fishery. on GOV.cn, 2012-05-01.
dc.relation.references[2] EU Must end overfishing to protect our oceans, say scientists, 2021-03-02.
dc.relation.references[3] Trade and Environment Database. Peruvian Anchovy Case: Anchovy Depletion and Trade. 2012-01-05.
dc.relation.references[4] Fishing, Costa Rica Experts. “Fishing Costa Rica”. web.archive.org/web/20210513144256/ https://www.costaricafishingexperts.com/2021-05-13.
dc.relation.references[5] Hritonenko N., Yatsenko Y. Mathematical Modeling in Economics, Ecology and the Environment. Springer (2016).
dc.relation.references[6] Lotka A. J. Elements of Physical Biology. Williams and Wilkins Company, Baltimore (1925).
dc.relation.references[7] Volterra V. Fluctuations in the Abundance of a Species considered Mathematically. Nature. 119, 12–13 (1926).
dc.relation.references[8] Hwang C. L., Fan L. T. A Discrete Version of Pontryagin’s Maximum Principle. Operations Research. 15 (1), 139–146 (1967).
dc.relation.references[9] https://www.aljazeera.net/news.29/09/2012.
dc.relation.references[10] Kar T. K., Chakraborty K. Bioeconomic modelling of a prey predator system using differential algebraic equations. International Journal of Engineering, Science and Technology. 2 (1), 13–34 (2010).
dc.relation.references[11] Dawes J. H. P., Souza M. O. A derivation of Holling’s type I, II and III functional responses in predator prey systems. Journal of Theoretical Biology. 327, 11–22 (2013).
dc.relation.references[12] Chouayakh K., El Bekkali C., El Foutayeni Y., Khaladi M., Rachik M. Maximization of the Fishermen’s Profits Exploiting a Fish Population in Several Fishery Zones. International Journal of Science and Research. 4 (1), 1141–1147 (2015).
dc.relation.references[13] Qi Y., Zhu Y. The study of global stability of a diffusive Holling–Tanner predator–prey model. Applied Mathematics Letters. 57, 132–138 (2016).
dc.relation.references[14] Mchich R., Charouki N., Auger P., Raissi N., Ettahiri O. Optimal spatial distribution of the fishing effort in a multi fishing zone model. Ecological Modelling. 197 (3–4), 274–280 (2006).
dc.relation.references[15] Lu Y., Pawelek K. A., Liu S. A stage-structured predator-prey model with predation over juvenile prey. Applied Mathematics and Computation. 297, 115–130 (2017).
dc.relation.references[16] Mbava W., Mugisha J. Y. T., Gonsalves J. W. Prey, predator and super-predator model with disease in the super-predator. Applied Mathematics and Computation. 297, 92–114 (2017).
dc.relation.references[17] Santra P., Mahapatra G. S., Pal D. Analysis of differential-algebraic prey–predator dynamical model with super predator harvesting on economic perspective. International Journal of Dynamics and Control. 4, 266–274 (2016).
dc.relation.references[18] Wikipedia. Discrete Laplace operator, http://en.wikipedia.org/wiki/Discrete Laplace operator (2007).
dc.relation.references[19] McAsey M., Mou L., Han W. Convergence of the forward-backward sweep method in optimal control. Computational Optimization and Applications. 53, 207–226 (2012).
dc.relation.referencesen[1] Hui L. Pollution, overfishing destroy East China Sea fishery. on GOV.cn, 2012-05-01.
dc.relation.referencesen[2] EU Must end overfishing to protect our oceans, say scientists, 2021-03-02.
dc.relation.referencesen[3] Trade and Environment Database. Peruvian Anchovy Case: Anchovy Depletion and Trade. 2012-01-05.
dc.relation.referencesen[4] Fishing, Costa Rica Experts. "Fishing Costa Rica". web.archive.org/web/20210513144256/ https://www.costaricafishingexperts.com/2021-05-13.
dc.relation.referencesen[5] Hritonenko N., Yatsenko Y. Mathematical Modeling in Economics, Ecology and the Environment. Springer (2016).
dc.relation.referencesen[6] Lotka A. J. Elements of Physical Biology. Williams and Wilkins Company, Baltimore (1925).
dc.relation.referencesen[7] Volterra V. Fluctuations in the Abundance of a Species considered Mathematically. Nature. 119, 12–13 (1926).
dc.relation.referencesen[8] Hwang C. L., Fan L. T. A Discrete Version of Pontryagin’s Maximum Principle. Operations Research. 15 (1), 139–146 (1967).
dc.relation.referencesen[9] https://www.aljazeera.net/news.29/09/2012.
dc.relation.referencesen[10] Kar T. K., Chakraborty K. Bioeconomic modelling of a prey predator system using differential algebraic equations. International Journal of Engineering, Science and Technology. 2 (1), 13–34 (2010).
dc.relation.referencesen[11] Dawes J. H. P., Souza M. O. A derivation of Holling’s type I, II and III functional responses in predator prey systems. Journal of Theoretical Biology. 327, 11–22 (2013).
dc.relation.referencesen[12] Chouayakh K., El Bekkali C., El Foutayeni Y., Khaladi M., Rachik M. Maximization of the Fishermen’s Profits Exploiting a Fish Population in Several Fishery Zones. International Journal of Science and Research. 4 (1), 1141–1147 (2015).
dc.relation.referencesen[13] Qi Y., Zhu Y. The study of global stability of a diffusive Holling–Tanner predator–prey model. Applied Mathematics Letters. 57, 132–138 (2016).
dc.relation.referencesen[14] Mchich R., Charouki N., Auger P., Raissi N., Ettahiri O. Optimal spatial distribution of the fishing effort in a multi fishing zone model. Ecological Modelling. 197 (3–4), 274–280 (2006).
dc.relation.referencesen[15] Lu Y., Pawelek K. A., Liu S. A stage-structured predator-prey model with predation over juvenile prey. Applied Mathematics and Computation. 297, 115–130 (2017).
dc.relation.referencesen[16] Mbava W., Mugisha J. Y. T., Gonsalves J. W. Prey, predator and super-predator model with disease in the super-predator. Applied Mathematics and Computation. 297, 92–114 (2017).
dc.relation.referencesen[17] Santra P., Mahapatra G. S., Pal D. Analysis of differential-algebraic prey–predator dynamical model with super predator harvesting on economic perspective. International Journal of Dynamics and Control. 4, 266–274 (2016).
dc.relation.referencesen[18] Wikipedia. Discrete Laplace operator, http://en.wikipedia.org/wiki/Discrete Laplace operator (2007).
dc.relation.referencesen[19] McAsey M., Mou L., Han W. Convergence of the forward-backward sweep method in optimal control. Computational Optimization and Applications. 53, 207–226 (2012).
dc.relation.urihttps://www.costaricafishingexperts.com/2021-05-13
dc.relation.urihttps://www.aljazeera.net/news.29/09/2012
dc.relation.urihttp://en.wikipedia.org/wiki/Discrete
dc.rights.holder© Національний університет “Львівська політехніка”, 2024
dc.subjectздобич–хижак
dc.subjectпросторово-часова дискретна модель
dc.subjectоптимальне керування
dc.subjectпринцип максимуму Понтрягіна
dc.subjectprey–predator
dc.subjectspatiotemporal discrete model
dc.subjectoptimal control
dc.subjectPontryagin’s maximum principle
dc.titleOptimal control problem of a discrete spatiotemporal prey-predator three-species fishery model
dc.title.alternativeПроблема оптимального керування дискретною просторово-часовою моделлю рибальства “жертва–хижак” трьох видів
dc.typeArticle

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Mathematical Modeling And Computing. – 2024. – Vol. 11, No. 2