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 |
Published: |
Emerald Publishing
2025-01-01
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Series: | Arab Journal of Mathematical Sciences |
Subjects: | |
Online Access: | https://www.emerald.com/insight/content/doi/10.1108/AJMS-03-2022-0052/full/pdf |
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Summary: | 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. |
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ISSN: | 1319-5166 2588-9214 |