A dynamic analysis of a prey–predator population model with a nonlinear harvesting rate
Purpose – In this article, the author discusses dynamical behaviors of a prey-predator population model with nonlinear harvesting rate and offers a mathematical analysis of the model. Design/methodology/approach – The design is by using modelization of populations interaction, qualitative theory of...
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2025-01-01
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| Series: | Arab Journal of Mathematical Sciences |
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| Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-03-2022-0052/full/pdf |
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| author | Nadia Mohdeb |
| author_facet | Nadia Mohdeb |
| author_sort | Nadia Mohdeb |
| collection | DOAJ |
| description | Purpose – In this article, the author discusses dynamical behaviors of a prey-predator population model with nonlinear harvesting rate and offers a mathematical analysis of the model. Design/methodology/approach – The design is by using modelization of populations interaction, qualitative theory of ordinary différential equations, bifurcations analysis, invariant center manifolds theory and Dulac's criterion. Findings – The author studies the stability of solutions and the existence of periodic solutions in the model, and proves the existence of some invariant sets and the production of a transcritical together with a saddle-node bifurcation. Practical implications – The author studies the effects of harvesting on the persistence and extinction properties and its influence in the perspectives of economic views. Originality/value – The authors considers a predator–prey model with a new nonlinear form of harvesting rate. The author’s intention is to make conceptual adjustments to a well-known predator–prey model in order to incorporate the effects of harvesting. |
| format | Article |
| id | doaj-art-cc262d7958ec47f5b4ab0dfb7fd065e7 |
| institution | Kabale University |
| issn | 1319-5166 2588-9214 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj-art-cc262d7958ec47f5b4ab0dfb7fd065e72025-01-24T04:22:17ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662588-92142025-01-01311476010.1108/AJMS-03-2022-0052A dynamic analysis of a prey–predator population model with a nonlinear harvesting rateNadia Mohdeb0Applied Mathematics Laboratory, University of Bejaia, Bejaia, AlgeriaPurpose – In this article, the author discusses dynamical behaviors of a prey-predator population model with nonlinear harvesting rate and offers a mathematical analysis of the model. Design/methodology/approach – The design is by using modelization of populations interaction, qualitative theory of ordinary différential equations, bifurcations analysis, invariant center manifolds theory and Dulac's criterion. Findings – The author studies the stability of solutions and the existence of periodic solutions in the model, and proves the existence of some invariant sets and the production of a transcritical together with a saddle-node bifurcation. Practical implications – The author studies the effects of harvesting on the persistence and extinction properties and its influence in the perspectives of economic views. Originality/value – The authors considers a predator–prey model with a new nonlinear form of harvesting rate. The author’s intention is to make conceptual adjustments to a well-known predator–prey model in order to incorporate the effects of harvesting.https://www.emerald.com/insight/content/doi/10.1108/AJMS-03-2022-0052/full/pdfStabilityForward bifurcationPersistent and permanentHarvestingLimit cycleStrong and center manifolds |
| spellingShingle | Nadia Mohdeb A dynamic analysis of a prey–predator population model with a nonlinear harvesting rate Arab Journal of Mathematical Sciences Stability Forward bifurcation Persistent and permanent Harvesting Limit cycle Strong and center manifolds |
| title | A dynamic analysis of a prey–predator population model with a nonlinear harvesting rate |
| title_full | A dynamic analysis of a prey–predator population model with a nonlinear harvesting rate |
| title_fullStr | A dynamic analysis of a prey–predator population model with a nonlinear harvesting rate |
| title_full_unstemmed | A dynamic analysis of a prey–predator population model with a nonlinear harvesting rate |
| title_short | A dynamic analysis of a prey–predator population model with a nonlinear harvesting rate |
| title_sort | dynamic analysis of a prey predator population model with a nonlinear harvesting rate |
| topic | Stability Forward bifurcation Persistent and permanent Harvesting Limit cycle Strong and center manifolds |
| url | https://www.emerald.com/insight/content/doi/10.1108/AJMS-03-2022-0052/full/pdf |
| work_keys_str_mv | AT nadiamohdeb adynamicanalysisofapreypredatorpopulationmodelwithanonlinearharvestingrate AT nadiamohdeb dynamicanalysisofapreypredatorpopulationmodelwithanonlinearharvestingrate |