Stability analysis and Hopf bifurcation of a delayed prey–predator model with Hattaf–Yousfi functional response and Allee effect

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dc.citation.epage673
dc.citation.issue3
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage668
dc.contributor.affiliationУніверситет Хасана ІІ Касабланки
dc.contributor.affiliationHassan II University of Casablanca
dc.contributor.authorБузіан, С.
dc.contributor.authorЛотфі, Е. М.
dc.contributor.authorХаттаф, К.
dc.contributor.authorЮсфі, Н.
dc.contributor.authorBouziane, S.
dc.contributor.authorLotfi, E. M.
dc.contributor.authorHattaf, K.
dc.contributor.authorYousfi, N.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T12:17:36Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractЕфект Аллі є важливим явищем у контексті екології, що характеризується кореляцією між щільністю популяції та середньою індивідуальною пристосованістю популяції. У цій роботі досліджується вплив ефекту Аллі на динаміку сповільненої моделі “жертва–хижак” з функціональним відгуком Хаттафа–Юсфі. Спочатку доведено, що запропонована модель з ефектом Аллі є математично та екологічно коректною. Крім того, досліджено стійкість рівноваги та обговорено локальне існування біфуркації Хопфа.
dc.description.abstractThe Allee effect is an important phenomena in the context of ecology characterized by a correlation between population density and the mean individual fitness of a population. In this work, we examine the influences of Allee effect on the dynamics of a delayed prey–predator model with Hattaf–Yousfi functional response. We first prove that the proposed model with Allee effect is mathematically and ecologically well-posed. Moreover, we study the stability of equilibriums and discuss the local existence of Hopf bifurcation.
dc.format.extent668-673
dc.format.pages6
dc.identifier.citationStability analysis and Hopf bifurcation of a delayed prey–predator model with Hattaf–Yousfi functional response and Allee effect / S. Bouziane, E. M. Lotfi, K. Hattaf, N. Yousfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 3. — P. 668–673.
dc.identifier.citationenStability analysis and Hopf bifurcation of a delayed prey–predator model with Hattaf–Yousfi functional response and Allee effect / S. Bouziane, E. M. Lotfi, K. Hattaf, N. Yousfi // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 3. — P. 668–673.
dc.identifier.doidoi.org/10.23939/mmc2023.03.668
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63539
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 3 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 3 (10), 2023
dc.relation.references[1] Lotka A. J. Elements of physical biology. Williams and Wilkins (1925).
dc.relation.references[2] Volterra V. Fluctuations in the abundance of a species considered mathematically. Nature. 118, 558–560 (1926).
dc.relation.references[3] Bouziane S., Lotfi E., Hattaf K., Yousfi N. Dynamics of a delayed prey–predator model with Hattaf–Yousfi functional response. Communications in Mathematical Biology and Neuroscience. 2022, 104 (2022).
dc.relation.references[4] Louartassi Y., Alla A., Hattaf K., Nabil A. Dynamics of a predator–prey model with harvesting and reserve area for prey in the presence of competition and toxicity. Journal of Applied Mathematics and Computing. 59, 305–321 (2019).
dc.relation.references[5] Allee W. C. Animal aggregations: A study in general sociology. Chicago, The University of Chicago Press (1931).
dc.relation.references[6] Pal P. J., Saha T., Sen M., Banerjee M. A delayed predator–prey model with strong Allee effect in prey population growth. Nonlinear Dynamics. 68, 23–42 (2012).
dc.relation.references[7] Ye Y., Liu H., Wei Y., Zhang K., Ma M., Ye J. Dynamic study of a predator-prey model with Allee effect and Holling type-I functional response. Advances in Difference Equations. 2019, 369 (2019).
dc.relation.references[8] Holling C. S. The components of predation as revealed by a study of small mammal predation of the European pine sawfly. The Canadian Entomologist. 91 (5), 293–320 (1959).
dc.relation.references[9] Garain K., Mandal P. S. Bubbling and hydra effect in a population system with Allee effect. Ecological Complexity. 47, 100939 (2021).
dc.relation.references[10] Hattaf K., Yousfi N. A class of delayed viral infection models with general incidence rate and adaptive immune response. International Journal of Dynamics and Control. 4, 254–265 (2016).
dc.relation.references[11] Hattaf K. A new generalized definition of fractional derivative with non-singular kernel. Computation. 8 (2), 49 (2020).
dc.relation.references[12] Hattaf K. On the stability and numerical scheme of fractional differential equations with application to biology. Computation. 10 (6), 97 (2022).
dc.relation.references[13] Berec L., Angulo E., Courchamp F. Multiple Allee effects and population management. Trends in Ecology and Evolution. 22 (4), 185–191 (2007).
dc.relation.references[14] Angulo E., Roemer G. W., Berec L., Gascoigne J., Courchamp F. Double Allee effects and extinction in the island fox. Conservation Biology. 21 (4), 1082–1091 (2007).
dc.relation.referencesen[1] Lotka A. J. Elements of physical biology. Williams and Wilkins (1925).
dc.relation.referencesen[2] Volterra V. Fluctuations in the abundance of a species considered mathematically. Nature. 118, 558–560 (1926).
dc.relation.referencesen[3] Bouziane S., Lotfi E., Hattaf K., Yousfi N. Dynamics of a delayed prey–predator model with Hattaf–Yousfi functional response. Communications in Mathematical Biology and Neuroscience. 2022, 104 (2022).
dc.relation.referencesen[4] Louartassi Y., Alla A., Hattaf K., Nabil A. Dynamics of a predator–prey model with harvesting and reserve area for prey in the presence of competition and toxicity. Journal of Applied Mathematics and Computing. 59, 305–321 (2019).
dc.relation.referencesen[5] Allee W. C. Animal aggregations: A study in general sociology. Chicago, The University of Chicago Press (1931).
dc.relation.referencesen[6] Pal P. J., Saha T., Sen M., Banerjee M. A delayed predator–prey model with strong Allee effect in prey population growth. Nonlinear Dynamics. 68, 23–42 (2012).
dc.relation.referencesen[7] Ye Y., Liu H., Wei Y., Zhang K., Ma M., Ye J. Dynamic study of a predator-prey model with Allee effect and Holling type-I functional response. Advances in Difference Equations. 2019, 369 (2019).
dc.relation.referencesen[8] Holling C. S. The components of predation as revealed by a study of small mammal predation of the European pine sawfly. The Canadian Entomologist. 91 (5), 293–320 (1959).
dc.relation.referencesen[9] Garain K., Mandal P. S. Bubbling and hydra effect in a population system with Allee effect. Ecological Complexity. 47, 100939 (2021).
dc.relation.referencesen[10] Hattaf K., Yousfi N. A class of delayed viral infection models with general incidence rate and adaptive immune response. International Journal of Dynamics and Control. 4, 254–265 (2016).
dc.relation.referencesen[11] Hattaf K. A new generalized definition of fractional derivative with non-singular kernel. Computation. 8 (2), 49 (2020).
dc.relation.referencesen[12] Hattaf K. On the stability and numerical scheme of fractional differential equations with application to biology. Computation. 10 (6), 97 (2022).
dc.relation.referencesen[13] Berec L., Angulo E., Courchamp F. Multiple Allee effects and population management. Trends in Ecology and Evolution. 22 (4), 185–191 (2007).
dc.relation.referencesen[14] Angulo E., Roemer G. W., Berec L., Gascoigne J., Courchamp F. Double Allee effects and extinction in the island fox. Conservation Biology. 21 (4), 1082–1091 (2007).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectекологія
dc.subjectефект Аллі
dc.subjectфункціональний відгук Хаттаф–Юсфі
dc.subjectстійкість
dc.subjectбіфуркація Хопфа
dc.subjectecology
dc.subjectAllee effect
dc.subjectHattaf–Yousfi functional response
dc.subjectstability
dc.subjectHopf bifurcation
dc.titleStability analysis and Hopf bifurcation of a delayed prey–predator model with Hattaf–Yousfi functional response and Allee effect
dc.title.alternativeАналіз стійкості та біфуркація Хопфа сповільненої моделі “жертва–хижак” з функціональним відгуком Хаттафа–Юсфі та ефектом Аллі
dc.typeArticle

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Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 3