Study of two species prey–predator model in imprecise environment with harvesting scenario

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dc.citation.epage398
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage385
dc.contributor.affiliationІнженерно-технологічний коледж, Інститут науки і техніки SRM
dc.contributor.affiliationCollege of Engineering and Technology, SRM Institute of Science and Technology
dc.contributor.authorВіджаялакшмі, Т.
dc.contributor.authorСентхамарай, Р.
dc.contributor.authorVijayalakshmi, T.
dc.contributor.authorSenthamarai, R.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T11:14:24Z
dc.date.created2022-02-28
dc.date.issued2022-02-28
dc.description.abstractУ цьому дослідженні пропонується та досліджується модель “хижак–жертва”, в якій є функціональна реакція здобування на групову поведінку “жертва–хижак”. Досліджено нелінійну модель росту “жертва–хижак” двох видів. Запропонована модель підтверджена теоретичними та чисельними результатами. Деякі числові описи подані для пояснення отримання аналітичних та теоретичних висновків. Для всіх можливих значень параметрів, які з’являються в системі “жертва–хижак”, розв’язано представлену модель як за допомогою варіаційного ітераційного методу (ВІМ) так і методом гомотопних збурень (МГЗ). Також використано кодування MATLAB, щоб порівняти отримані наближені аналітичні вирази з результатами комп’ютерного моделювання. Виявлено, що суттєвої різниці між аналітичними та чисельними результатами немає.
dc.description.abstractThis study proposes and explores a prey–predator model that presents a functional response to group behavior of prey–predator harvesting. We study a non-linear model of prey–predator growths in two species. The proposed model is supported by theoretical and numerical results. Some numerical descriptions are provided to help our analytical and theoretical conclusions. For all possible parameter values occurring in a prey–predator system, we solved it by using both VIM (variational iteration method) and HPM (homotopy perturbation method). We also used MATLAB coding to compare our approximate analytical expressions with numerical simulations. We have found that there is no significant difference when comparing analytical and numerical results.
dc.format.extent385-398
dc.format.pages14
dc.identifier.citationVijayalakshmi T. Study of two species prey–predator model in imprecise environment with harvesting scenario / T. Vijayalakshmi, R. Senthamarai // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 2. — P. 385–398.
dc.identifier.citationenVijayalakshmi T. Study of two species prey–predator model in imprecise environment with harvesting scenario / T. Vijayalakshmi, R. Senthamarai // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 2. — P. 385–398.
dc.identifier.doidoi.org/10.23939/mmc2022.02.385
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63439
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 2 (9), 2022
dc.relation.ispartofMathematical Modeling and Computing, 2 (9), 2022
dc.relation.references[1] Liu L., Meng X. Optimal harvesting control and dynamics of two-species stochastic model with delays. Advances in Difference Equations. 2017, Article number: 18 (2017).
dc.relation.references[2] Souna F., Lakmechea A., Djilali S. Spatiotemporal patterns in a diffusive predator-prey model with protection zone and predator harvesting. Chaos, Solitons & Fractals. 140, 110180 (2020).
dc.relation.references[3] Liu G., Wang X., Meng X., Gao S. Extinction and persistence in mean of a novel delay impulsive stochastic infected predator-prey system with jumps. Complexity. 2017, 1950970 (2017).
dc.relation.references[4] Bian F., Zhao W., Song Y., Yue R. Dynamical analysis of a class of prey-predator model with BeddingtonDeangelis functional response, stochastic perturbation, and impulsive toxicant input. Complexity. 2017, 3742197 (2017).
dc.relation.references[5] Sahoo B., Das B., Samanta S. Dynamics of harvested-predator–prey model: role of alternative resources. Modeling Earth Systems and Environment. 2, 140 (2016).
dc.relation.references[6] Vijayalakshmi T., Senthamarai R. An analytical approach to the density dependent prey-predator system with Beddington — deangelies functional response. AIP Conference Proceedings. 2112, 020077 (2019).
dc.relation.references[7] Meng X.-Y., Qin N.-N., Huo H.-F. Dynamics analysis of a predator–prey system with harvesting prey and disease in prey species. Journal of Biological Dynamics. 12, 342–374 (2018).
dc.relation.references[8] Das K. A study of harvesting in a predator–prey model with disease in both populations. Mathematical Methods in the Applied Sciences. 39, 2853–2870 (2016).
dc.relation.references[9] Senthamarai R., Vijayalakshmi T. An analytical approach to top predator interference on the dynamics of a food chain model. Journal of Physics: Conference Series. 1000, 012139 (2018).
dc.relation.references[10] Das A., Pal M. Theoretical analysis of an imprecise prey-predator model with harvesting and optimal control. Journal of Optimization. 2019, 9512879 (2019).
dc.relation.references[11] Van Voorn G. A. K., Kooi B. W. Combining bifurcation and sensitivity analysis for ecological models. The European Physical Journal Special Topics. 226, 2101–2118 (2017).
dc.relation.references[12] Yu D.-N., He J.-H., Garcia A. G. Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators. Journal of Low Frequency Noise, Vibration and Active Control. 38 (3–4), 1540–1554 (2019).
dc.relation.references[13] Shirejini S. Z., Fattahi M. Mathematical modeling and analytical solution of two-phase flow transport in an immobilized-cell photo bioreactor using the homotopy perturbation method (HPM). International Journal of Hydrogen Energy. 41 (41), 18405–18417 (2016).
dc.relation.references[14] Sivakumar M., Senthamarai R. Mathematical Model of Epidemics: SEIR Model by using Homotopy Perturbation Method. AIP Conference Proceedings. 2112, 020080 (2019).
dc.relation.references[15] Nivethitha M., Senthamarai R. Analytical approach to a steady-state predator-prey system of Lotka–Volterra model. AIP Conference Proceedings. 2277, 210005 (2020).
dc.relation.references[16] Sivakumar M., Senthamarai R. Mathematical model of epidemics: Analytical approach to SIRW model using homotopy perturbation method. AIP Conference Proceedings. 2277, 1–8 (2020).
dc.relation.references[17] Vijayalakshmi T., Senthamarai R. Application of homotopy perturbation and variational iteration methods for nonlinear imprecise prey–predator model with stability analysis. The Journal of Supercomputing. 78, 2477–2502 (2021).
dc.relation.references[18] Ghorbani A. Approximate solution of delay differential equations via variational iteration method. Nonlinear science letters. A, Mathematics, physics and mechanics. 8 (2), 236–239 (2017).
dc.relation.references[19] Anjum N., He J.-H. Laplace transform: Making the variational iteration method easier. Applied Mathematics Letters. 92, 134–138 (2019).
dc.relation.references[20] Senthamarai R., Saibavani T. N. Substrate mass transfer: analytical approach for immobilized enzyme reactions. Journal of Physics: Conference Series. 1000, 012146 (2018).
dc.relation.referencesen[1] Liu L., Meng X. Optimal harvesting control and dynamics of two-species stochastic model with delays. Advances in Difference Equations. 2017, Article number: 18 (2017).
dc.relation.referencesen[2] Souna F., Lakmechea A., Djilali S. Spatiotemporal patterns in a diffusive predator-prey model with protection zone and predator harvesting. Chaos, Solitons & Fractals. 140, 110180 (2020).
dc.relation.referencesen[3] Liu G., Wang X., Meng X., Gao S. Extinction and persistence in mean of a novel delay impulsive stochastic infected predator-prey system with jumps. Complexity. 2017, 1950970 (2017).
dc.relation.referencesen[4] Bian F., Zhao W., Song Y., Yue R. Dynamical analysis of a class of prey-predator model with BeddingtonDeangelis functional response, stochastic perturbation, and impulsive toxicant input. Complexity. 2017, 3742197 (2017).
dc.relation.referencesen[5] Sahoo B., Das B., Samanta S. Dynamics of harvested-predator–prey model: role of alternative resources. Modeling Earth Systems and Environment. 2, 140 (2016).
dc.relation.referencesen[6] Vijayalakshmi T., Senthamarai R. An analytical approach to the density dependent prey-predator system with Beddington - deangelies functional response. AIP Conference Proceedings. 2112, 020077 (2019).
dc.relation.referencesen[7] Meng X.-Y., Qin N.-N., Huo H.-F. Dynamics analysis of a predator–prey system with harvesting prey and disease in prey species. Journal of Biological Dynamics. 12, 342–374 (2018).
dc.relation.referencesen[8] Das K. A study of harvesting in a predator–prey model with disease in both populations. Mathematical Methods in the Applied Sciences. 39, 2853–2870 (2016).
dc.relation.referencesen[9] Senthamarai R., Vijayalakshmi T. An analytical approach to top predator interference on the dynamics of a food chain model. Journal of Physics: Conference Series. 1000, 012139 (2018).
dc.relation.referencesen[10] Das A., Pal M. Theoretical analysis of an imprecise prey-predator model with harvesting and optimal control. Journal of Optimization. 2019, 9512879 (2019).
dc.relation.referencesen[11] Van Voorn G. A. K., Kooi B. W. Combining bifurcation and sensitivity analysis for ecological models. The European Physical Journal Special Topics. 226, 2101–2118 (2017).
dc.relation.referencesen[12] Yu D.-N., He J.-H., Garcia A. G. Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators. Journal of Low Frequency Noise, Vibration and Active Control. 38 (3–4), 1540–1554 (2019).
dc.relation.referencesen[13] Shirejini S. Z., Fattahi M. Mathematical modeling and analytical solution of two-phase flow transport in an immobilized-cell photo bioreactor using the homotopy perturbation method (HPM). International Journal of Hydrogen Energy. 41 (41), 18405–18417 (2016).
dc.relation.referencesen[14] Sivakumar M., Senthamarai R. Mathematical Model of Epidemics: SEIR Model by using Homotopy Perturbation Method. AIP Conference Proceedings. 2112, 020080 (2019).
dc.relation.referencesen[15] Nivethitha M., Senthamarai R. Analytical approach to a steady-state predator-prey system of Lotka–Volterra model. AIP Conference Proceedings. 2277, 210005 (2020).
dc.relation.referencesen[16] Sivakumar M., Senthamarai R. Mathematical model of epidemics: Analytical approach to SIRW model using homotopy perturbation method. AIP Conference Proceedings. 2277, 1–8 (2020).
dc.relation.referencesen[17] Vijayalakshmi T., Senthamarai R. Application of homotopy perturbation and variational iteration methods for nonlinear imprecise prey–predator model with stability analysis. The Journal of Supercomputing. 78, 2477–2502 (2021).
dc.relation.referencesen[18] Ghorbani A. Approximate solution of delay differential equations via variational iteration method. Nonlinear science letters. A, Mathematics, physics and mechanics. 8 (2), 236–239 (2017).
dc.relation.referencesen[19] Anjum N., He J.-H. Laplace transform: Making the variational iteration method easier. Applied Mathematics Letters. 92, 134–138 (2019).
dc.relation.referencesen[20] Senthamarai R., Saibavani T. N. Substrate mass transfer: analytical approach for immobilized enzyme reactions. Journal of Physics: Conference Series. 1000, 012146 (2018).
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.subjectматематичне моделювання
dc.subjectздобута здобич – хижак
dc.subjectточне значення
dc.subjectчисельне моделювання
dc.subjectваріаційний ітераційний метод
dc.subjectметод гомотопних збурень
dc.subjectmathematical modeling
dc.subjectharvested prey–predator
dc.subjectprecise value
dc.subjectnumerical simulation
dc.subjectvariational iteration method
dc.subjecthomotopy perturbation method
dc.titleStudy of two species prey–predator model in imprecise environment with harvesting scenario
dc.title.alternativeДослідження моделі “жертва–хижак” двох видів у неточному середовищі зі сценарієм здобування
dc.typeArticle

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Mathematical Modeling And Computing. – 2022. – Vol. 9, No. 2