Prey–predator optimal harvesting mathematical model in the presence of toxic prey under interval uncertainty
This paper explores a multispecies prey–predator harvesting system based on Lotka–Volterra model with two preys (palatable and toxic prey) and one predator with interval biological parameters. Due to the enhancement in resource availability, prey–predator system becomes destabilized theoretically (t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-09-01
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| Series: | Scientific African |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2468227623002934 |
| _version_ | 1797676194835988480 |
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| author | M. Mukherjee D. Pal S.K. Mahato Ebenezer Bonyah |
| author_facet | M. Mukherjee D. Pal S.K. Mahato Ebenezer Bonyah |
| author_sort | M. Mukherjee |
| collection | DOAJ |
| description | This paper explores a multispecies prey–predator harvesting system based on Lotka–Volterra model with two preys (palatable and toxic prey) and one predator with interval biological parameters. Due to the enhancement in resource availability, prey–predator system becomes destabilized theoretically (the paradox of enrichment). Also, a prey may become toxic for the predator due to a little change in the resource stoichiometry. The presence of toxic prey influences the growth of the predator as well as that of a palatable prey. Thus the dynamics of prey–predator system is significantly affected by the presence of such toxic prey. Again, due to lack of precise numerical data of the biological parameters an interval number based mathematical toxic prey–predator model is developed and then discussed the dynamical behaviour of the model. Then, we observe the existence of different points of equilibrium and also the stabilities at these points of equilibrium of the system are presented. Also, the bionomic equilibrium of the harvesting model has been analysed. Next, the optimal harvest policy is carried out and obtained the solution in the interior equilibrium point using Pontryagin’s maximum principle. All important analytical findings are demonstrated through computer simulation using MATLAB followed by discussions and conclusions. |
| first_indexed | 2024-03-11T22:25:29Z |
| format | Article |
| id | doaj.art-060a48d314ff413d962e116b53073466 |
| institution | Directory Open Access Journal |
| issn | 2468-2276 |
| language | English |
| last_indexed | 2024-03-11T22:25:29Z |
| publishDate | 2023-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Scientific African |
| spelling | doaj.art-060a48d314ff413d962e116b530734662023-09-24T05:16:17ZengElsevierScientific African2468-22762023-09-0121e01837Prey–predator optimal harvesting mathematical model in the presence of toxic prey under interval uncertaintyM. Mukherjee0D. Pal1S.K. Mahato2Ebenezer Bonyah3Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, West Bengal 723104, IndiaChandrahati Dilip Kumar High School (H.S.), Chandrahati 712504, West Bengal, IndiaDepartment of Mathematics, Sidho-Kanho-Birsha University, Purulia, West Bengal 723104, IndiaDepartment of Mathematics Education, Akenten Appiah Menka University of Skills Training and Entrepreneurial Development, Kumasi, Ghana; Corresponding author.This paper explores a multispecies prey–predator harvesting system based on Lotka–Volterra model with two preys (palatable and toxic prey) and one predator with interval biological parameters. Due to the enhancement in resource availability, prey–predator system becomes destabilized theoretically (the paradox of enrichment). Also, a prey may become toxic for the predator due to a little change in the resource stoichiometry. The presence of toxic prey influences the growth of the predator as well as that of a palatable prey. Thus the dynamics of prey–predator system is significantly affected by the presence of such toxic prey. Again, due to lack of precise numerical data of the biological parameters an interval number based mathematical toxic prey–predator model is developed and then discussed the dynamical behaviour of the model. Then, we observe the existence of different points of equilibrium and also the stabilities at these points of equilibrium of the system are presented. Also, the bionomic equilibrium of the harvesting model has been analysed. Next, the optimal harvest policy is carried out and obtained the solution in the interior equilibrium point using Pontryagin’s maximum principle. All important analytical findings are demonstrated through computer simulation using MATLAB followed by discussions and conclusions.http://www.sciencedirect.com/science/article/pii/S2468227623002934Prey–predatorFood toxicityStabilityOptimal harvest policyBionomic equilibriumImprecise parameters |
| spellingShingle | M. Mukherjee D. Pal S.K. Mahato Ebenezer Bonyah Prey–predator optimal harvesting mathematical model in the presence of toxic prey under interval uncertainty Scientific African Prey–predator Food toxicity Stability Optimal harvest policy Bionomic equilibrium Imprecise parameters |
| title | Prey–predator optimal harvesting mathematical model in the presence of toxic prey under interval uncertainty |
| title_full | Prey–predator optimal harvesting mathematical model in the presence of toxic prey under interval uncertainty |
| title_fullStr | Prey–predator optimal harvesting mathematical model in the presence of toxic prey under interval uncertainty |
| title_full_unstemmed | Prey–predator optimal harvesting mathematical model in the presence of toxic prey under interval uncertainty |
| title_short | Prey–predator optimal harvesting mathematical model in the presence of toxic prey under interval uncertainty |
| title_sort | prey predator optimal harvesting mathematical model in the presence of toxic prey under interval uncertainty |
| topic | Prey–predator Food toxicity Stability Optimal harvest policy Bionomic equilibrium Imprecise parameters |
| url | http://www.sciencedirect.com/science/article/pii/S2468227623002934 |
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