Study of Hopf bifurcation of delayed tritrophic system: dinoflagellates, mussels, and crabs

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dc.citation.epage79
dc.citation.issue1
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage66
dc.contributor.affiliationУніверситет Хасана ІІ Касабланки
dc.contributor.affiliationHassan II University of Casablanca
dc.contributor.authorХафдане, М.
dc.contributor.authorАгмур, І.
dc.contributor.authorЕль Футаєні, Ю.
dc.contributor.authorHafdane, M.
dc.contributor.authorAgmour, I.
dc.contributor.authorEl Foutayeni, Y.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T11:54:53Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractУ статті розглянуто дискретну динамічну систему зі затримкою з трьома морськими видами: жертва, хижак та суперхижак. Враховано не лише ефект токсичності здобичі, але і негативний ефект надмірного ловіння перелічених видів. Дослідження моделі полягає в пошуку рівноваги за допомогою аналізу власних значень, існування біфуркацій Хопфа у внутрішніх рівновагах, визначення напрямку та аналізу стійкості біфуркації Хопфа з використанням теорії нормальної форми та центрального многовиду. Наведено декілька прикладів із чисельним моделюванням, які ілюструють результати для різних значень затримки.
dc.description.abstractIn this paper, we have a discrete delayed dynamic system of three marine species: prey, predator, and superpredator. In addition to the effect of prey toxicity, we consider the negative fishing effect of these species. The study of this model consists of the search for equilibria with eigenvalue analysis, the existence of Hopf bifurcations at interior equilibria, and the determination of direction and stability analysis of Hopf bifurcation using the theory of normal form and center manifold. Some examples are given with numerical simulations to illustrate the results in different cases of delay
dc.format.extent66-79
dc.format.pages14
dc.identifier.citationHafdane M. Study of Hopf bifurcation of delayed tritrophic system: dinoflagellates, mussels, and crabs / M. Hafdane, I. Agmour, Y. El Foutayeni // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 1. — P. 66–79.
dc.identifier.citationenHafdane M. Study of Hopf bifurcation of delayed tritrophic system: dinoflagellates, mussels, and crabs / M. Hafdane, I. Agmour, Y. El Foutayeni // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 1. — P. 66–79.
dc.identifier.doidoi.org/10.23939/mmc2023.01.066
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63501
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 1 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 1 (10), 2023
dc.relation.references[1] El Foutayeni Y., Bentounsi M., Agmour I., Achtaich N. Bioeconomic model of zooplankton–phytoplankton in the central area of Morocco. Modeling Earth Systems and Environment. 6, 461–469 (2020).
dc.relation.references[2] El Foutayeni Y., Khaladi M., Zegzouti A. Profit maximization of fishermen exploiting two fish species in competition. Amer. J. Comput. Appl. Math. to appear (2023).
dc.relation.references[3] El Foutayeni Y., Khaladi M. A generalized bio-economic model for competing multiple-fish populations where prices depend on harvest. Journal of Advanced Modeling and Optimization. 14 (3), 531–542 (2012).
dc.relation.references[4] El Foutayeni Y., Khaladi M. A bio-economic model of fishery where prices depend harvest. Journal of Advanced Modeling and Optimization. 14 (3), 543–555 (2012).
dc.relation.references[5] Bentounsi M., Agmour I., Achtaich N., El Foutayeni Y. The impact of price on the profits of fishermen exploiting tritrophic prey–predator fish populations. International Journal of Differential Equations. 13, 2381483 (2018).
dc.relation.references[6] Bentounsi M., Agmour I., Achtaich N., El Foutayeni Y. Intrinsic growth rates influence on the net economic rents of fishermen. International Journal of Dynamical Systems and Differential Equations. 9 (4), 362–379 (2019).
dc.relation.references[7] Agmour I., Achtaich N., El Foutayeni Y. Carrying capacity influence on the incomes of seiners exploiting marine species in the Atlantic coast of Morocco. Mathematical Biosciences. 305, 10–17 (2018).
dc.relation.references[8] Agmour I., Achtaich N., El Foutayeni Y. Stability analysis of a competing fish populations model with the presence of a predator. International Journal of Nonlinear Science. 26 (2), 108–121 (2018).
dc.relation.references[9] Bentounsi M., Agmour I., Achtaich N., El Foutayeni Y. The Hopf bifurcation and stability of delayed predator–prey system. Computational and Applied Mathematics. 37 (5), 5702–5714 (2018).
dc.relation.references[10] Song Y., Wei J. Bifurcation analysis for Chen’s System with delayed feedback and its application to Control of chaos. Chaos, Solitons & Fractals. 22 (1), 75–91 (2004).
dc.relation.references[11] Ruan S., Wei J. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dynamics of Continuous, Discrete & Impulsive Systems A. 10 (6), 863–874 (2003).
dc.relation.references[12] Hale J. K. Theory of Functional Differential Equations. Springer, New York (1977).
dc.relation.references[13] Hassard B. D., Kazarinoff N. D., Wan Y.-H. Theory and applications of hopf bifurcation. Cambridge University Press, Cambridge (1981).
dc.relation.referencesen[1] El Foutayeni Y., Bentounsi M., Agmour I., Achtaich N. Bioeconomic model of zooplankton–phytoplankton in the central area of Morocco. Modeling Earth Systems and Environment. 6, 461–469 (2020).
dc.relation.referencesen[2] El Foutayeni Y., Khaladi M., Zegzouti A. Profit maximization of fishermen exploiting two fish species in competition. Amer. J. Comput. Appl. Math. to appear (2023).
dc.relation.referencesen[3] El Foutayeni Y., Khaladi M. A generalized bio-economic model for competing multiple-fish populations where prices depend on harvest. Journal of Advanced Modeling and Optimization. 14 (3), 531–542 (2012).
dc.relation.referencesen[4] El Foutayeni Y., Khaladi M. A bio-economic model of fishery where prices depend harvest. Journal of Advanced Modeling and Optimization. 14 (3), 543–555 (2012).
dc.relation.referencesen[5] Bentounsi M., Agmour I., Achtaich N., El Foutayeni Y. The impact of price on the profits of fishermen exploiting tritrophic prey–predator fish populations. International Journal of Differential Equations. 13, 2381483 (2018).
dc.relation.referencesen[6] Bentounsi M., Agmour I., Achtaich N., El Foutayeni Y. Intrinsic growth rates influence on the net economic rents of fishermen. International Journal of Dynamical Systems and Differential Equations. 9 (4), 362–379 (2019).
dc.relation.referencesen[7] Agmour I., Achtaich N., El Foutayeni Y. Carrying capacity influence on the incomes of seiners exploiting marine species in the Atlantic coast of Morocco. Mathematical Biosciences. 305, 10–17 (2018).
dc.relation.referencesen[8] Agmour I., Achtaich N., El Foutayeni Y. Stability analysis of a competing fish populations model with the presence of a predator. International Journal of Nonlinear Science. 26 (2), 108–121 (2018).
dc.relation.referencesen[9] Bentounsi M., Agmour I., Achtaich N., El Foutayeni Y. The Hopf bifurcation and stability of delayed predator–prey system. Computational and Applied Mathematics. 37 (5), 5702–5714 (2018).
dc.relation.referencesen[10] Song Y., Wei J. Bifurcation analysis for Chen’s System with delayed feedback and its application to Control of chaos. Chaos, Solitons & Fractals. 22 (1), 75–91 (2004).
dc.relation.referencesen[11] Ruan S., Wei J. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dynamics of Continuous, Discrete & Impulsive Systems A. 10 (6), 863–874 (2003).
dc.relation.referencesen[12] Hale J. K. Theory of Functional Differential Equations. Springer, New York (1977).
dc.relation.referencesen[13] Hassard B. D., Kazarinoff N. D., Wan Y.-H. Theory and applications of hopf bifurcation. Cambridge University Press, Cambridge (1981).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectхижак–здобич
dc.subjectаналіз стійкості
dc.subjectбіфуркація Хопфа
dc.subjectдискретна затримка
dc.subjectрибальське зусилля
dc.subjectpredator–prey
dc.subjectstability analysis
dc.subjectHopf bifurcation
dc.subjectdiscrete delay
dc.subjectfishing effort
dc.titleStudy of Hopf bifurcation of delayed tritrophic system: dinoflagellates, mussels, and crabs
dc.title.alternativeДослідження біфуркації Хопфа для уповільненої тритрофної системи: динофлагеляти, мідії та краби
dc.typeArticle

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Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 1