Optimal control of tritrophic reaction–diffusion system with a spatiotemporal model

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dc.citation.epage662
dc.citation.issue3
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage647
dc.contributor.affiliationУніверситет Хасана ІІ Касабланки
dc.contributor.affiliationHassan II University of Casablanca
dc.contributor.authorБаала, Ю.
dc.contributor.authorАгмур, І.
dc.contributor.authorРачик, М.
dc.contributor.authorBaala, Y.
dc.contributor.authorAgmour, I.
dc.contributor.authorRachik, M.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T11:32:59Z
dc.date.created2022-02-28
dc.date.issued2022-02-28
dc.description.abstractУ цій статті пропонується нова модель просторово-часової динаміки, що стосується тритрофної реакційно-дифузійної системи, вводячи фітопланктон і зоопланктон. Нагадаємо, що фітопланктон і зоопланктон є основою морського харчового ланцюга. У кожній морській тритрофній системі є здобич. Основною метою цієї роботи є контроль біомаси цього виду для забезпечення стійкості системи. Щоб досягти цього, визначаємо оптимальний контроль, який мінімізує біомасу суперхижаків. У цій статті досліджується існування та стійкість внутрішньої точки рівноваги. Окрема увага надана характеристиці оптимального керування.
dc.description.abstractIn this paper, we propose a new model of spatio-temporal dynamics concerning the tritrophic reaction-diffusion system by introducing Phytoplankton and Zooplankton. We recall that the phytoplankton and zooplankton species are the basis of the marine food chain. There is prey in each marine tritrophic system. The main objective of this work is to control this species's biomass to ensure the system's sustainability. To achieve this, we determine an optimal control that minimizes the biomass of super predators. In this paper, we study the existence and stability of the interior equilibrium point. Then, we move to give the characterization of optimal control.
dc.format.extent647-662
dc.format.pages16
dc.identifier.citationBaala Y. Optimal control of tritrophic reaction–diffusion system with a spatiotemporal model / Y. Baala, I. Agmour, M. Rachik // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 647–662.
dc.identifier.citationenBaala Y. Optimal control of tritrophic reaction–diffusion system with a spatiotemporal model / Y. Baala, I. Agmour, M. Rachik // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 647–662.
dc.identifier.doidoi.org/10.23939/mmc2022.03.647
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63463
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 3 (9), 2022
dc.relation.ispartofMathematical Modeling and Computing, 3 (9), 2022
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dc.relation.references[20] Zhang X., Zhao H. Dynamics and pattern formation of a diffusive predator–prey model in the presence of toxicity. Nonlinear Dynamics. 95, 2163–2179 (2019).
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dc.relation.references[22] Aziz-Alaoui M. A., Daher Okiye M. Boundedness and global stability for a predator–prey model with modified Leslie–Gower and Holling type II shemes. Applied Mathematics Letters. 16 (7), 1069–1075 (2003).
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dc.relation.referencesen[1] Leslie P. H. Some further notes on the use of matrices in population mathematics. Biometrika. 35 (3–4), 213–245 (1948).
dc.relation.referencesen[2] Leslie P. H., Gower J. C. The properties of a stochastic model for the predator–prey type of interaction between two species. Biometrika. 47 (3–4), 219–234 (1960).
dc.relation.referencesen[3] Siez E., Gonz´alez-Olivares E. Dynamics of a predator–prey model. SIAM Journal on Applied Mathematics. 59 (5), 1867–1878 (2021).
dc.relation.referencesen[4] Ma Z.-P., Li W.-T. Bifurcation analysis on a diffusive Holling–Tanner predator–prey model. Applied Mathematical Modelling. 37 (6), 4371–4384 (2013).
dc.relation.referencesen[5] Li X., Jiang W., Shi J. Hopf bifurcation and Turing instability in the reaction–diffusion Holling–Tanner predatorprey model. IMA Journal of Applied Mathematics. 78 (2), 287–306 (2013).
dc.relation.referencesen[6] May R. M. Limit cycles in predator–prey communities. Science. 177 (4052), 900–902 (1972).
dc.relation.referencesen[7] Sun G.-Q., Zhang J., Song L.-P., Jin Z., Li B.-L. Pattern formation of a spatial predator–prey system. Applied Mathematics and Computation. 218 (22), 11151–11162 (2012).
dc.relation.referencesen[8] Mandal P. S., Banerjee M. Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model. Physica A: Statistical Mechanics and its Applications. 391 (4), 1216–1233 (2012).
dc.relation.referencesen[9] Chang L., Sun G.-Q., Wang Z., Jin Z. Rich dynamics in a spatial predator–prey model with delay. Applied Mathematics and Computation. 256, 540–550 (2015).
dc.relation.referencesen[10] Peixoto M. S., de Barros L. C., Bassanezi R. C. Predator–prey fuzzy model. Ecological Modelling. 214 (1), 39–44 (2008).
dc.relation.referencesen[11] Peixoto M. S., de Barros L. C., Bassanezi R. C. An approach via fuzzy sets theory for predator-prey model. Decision Making and Soft Computing. 9, 682–687 (2014).
dc.relation.referencesen[12] Yi F., Wei J., Shi J. Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator–prey system. Journal of Differential Equations. 246 (5), 1944–1977 (2009).
dc.relation.referencesen[13] Wang J., Shi J., Wei J. Dynamics and pattern formation in a diffusive predator–prey system with strong Allee effect in prey. Journal of Differential Equations. 251 (4–5), 1276–1304 (2011).
dc.relation.referencesen[14] Song Y., Jiang H., Yuan Y. Turing–Hopf bifurcation in the reaction-diffusion system with delay and application to a diffusive predator–prey model. Journal of Applied Analysis & Computation. 9 (3), 1132–1164 (2019).
dc.relation.referencesen[15] Cao X., Jiang W. Turing–Hopf bifurcation and spatiotemporal patterns in a diffusive predator–prey system with Crowley–Martin functional response. Nonlinear Analysis: Real World Applications. 43, 428–450 (2018).
dc.relation.referencesen[16] Chattopadhyay J. Effect of toxic substances on a two-species competitive system. Ecological Modelling. 84 (1–3), 287–289 (1996).
dc.relation.referencesen[17] Clark W. C. Mathematical Bioeconomics: The Optimal Management of Renewable Resources. WileyInterscience (1990).
dc.relation.referencesen[18] Cohen Y. Applications of control theory in ecology. Lecture Notes in Biomathematics. Berlin, Heidelberg, New York, Tokyo, Springer (1987).
dc.relation.referencesen[19] Wei X., Wei J. Turing instability and bifurcation analysis in a diffusive bimolecular system with delayed feedback. Communications in Nonlinear Science and Numerical Simulation. 50, 241–255 (2017).
dc.relation.referencesen[20] Zhang X., Zhao H. Dynamics and pattern formation of a diffusive predator–prey model in the presence of toxicity. Nonlinear Dynamics. 95, 2163–2179 (2019).
dc.relation.referencesen[21] Smoller J. Shock waves and reaction–diffusion equations. Vol. 258. Springer Science & Business Media, New York (2012).
dc.relation.referencesen[22] Aziz-Alaoui M. A., Daher Okiye M. Boundedness and global stability for a predator–prey model with modified Leslie–Gower and Holling type II shemes. Applied Mathematics Letters. 16 (7), 1069–1075 (2003).
dc.relation.referencesen[23] Daher Okiye M., Aziz-Alaoui M. A. On the dynamics of a predator–prey model with the Holling–Tanner functional response. 270–278. MIRIAM Editions, Proc. ESMTB conf. (2002).
dc.relation.referencesen[24] Brezis H., Ciarlet P. G., Lions J. L. Analyse fonctionnelle: theorie et applications. Vol. 91. Dunod Paris (1999).
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.subjectпросторово-часова динаміка
dc.subjectреакційно-дифузійна система
dc.subjectоптимальне керування
dc.subjectмаксимізація
dc.subjectстійкість
dc.subjectspatio-temporal dynamics
dc.subjectreaction-diffusion system
dc.subjectoptimal control
dc.subjectmaximizing
dc.subjectstability
dc.titleOptimal control of tritrophic reaction–diffusion system with a spatiotemporal model
dc.title.alternativeОптимальне керування тритрофною реакційно-дифузійною системою за допомогою просторово-часової моделі
dc.typeArticle

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Mathematical Modeling And Computing. – 2022. – Vol. 9, No. 3