Dynamics Analysis and Optimality in Selective Harvesting Predator-Prey Model With Modified Leslie-Gower and Holling-Type II
In this work, we consider the optimal harvesting and stability problems of a prey-predator model with modified Leslie-Gower and Holling-type II functional response. The model is governed by a system of three differential equations which describe the interactions between prey, predator and harvesting...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2019-03-01
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| Series: | Nonautonomous Dynamical Systems |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/msds-2019-0001 |
| _version_ | 1818733994953408512 |
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| author | Abid W. Yafia R. Aziz-Alaoui M. A. Aghriche Ahmed |
| author_facet | Abid W. Yafia R. Aziz-Alaoui M. A. Aghriche Ahmed |
| author_sort | Abid W. |
| collection | DOAJ |
| description | In this work, we consider the optimal harvesting and stability problems of a prey-predator model with modified Leslie-Gower and Holling-type II functional response. The model is governed by a system of three differential equations which describe the interactions between prey, predator and harvesting effort. Boundedness and existence of solutions for this system are showed. The existence and local stability of the possible steady states are analyzed and the conditions of global stability of the interior equilibrium are established by using the Lyapunov function, we prove also the occurrence of Hopf bifurcation at this point. By using the Pontryagin’s maximal principle, we formulate and we solve the problem of the optimal harvest policy. In the end, some numerical simulations are given to support our theoretical results. |
| first_indexed | 2024-12-17T23:58:19Z |
| format | Article |
| id | doaj.art-d993494e3ab341cd9f2c7928c513960f |
| institution | Directory Open Access Journal |
| issn | 2353-0626 |
| language | English |
| last_indexed | 2024-12-17T23:58:19Z |
| publishDate | 2019-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonautonomous Dynamical Systems |
| spelling | doaj.art-d993494e3ab341cd9f2c7928c513960f2022-12-21T21:28:01ZengDe GruyterNonautonomous Dynamical Systems2353-06262019-03-016111710.1515/msds-2019-0001msds-2019-0001Dynamics Analysis and Optimality in Selective Harvesting Predator-Prey Model With Modified Leslie-Gower and Holling-Type IIAbid W.0Yafia R.1Aziz-Alaoui M. A.2Aghriche Ahmed3Laboratoire d’ingenierie Mathématiquede l’ecole polytechnique de TunisIbn Tofail Universit, Faculty of Sciences, Department of Mathematics, Campus Universitaire, BP 133, Kénitra, MoroccoLMAH, FR-CNRS-3335, Université du Havre Normandie, 25 Rue Ph. Lebon, BP:540, 76058Le Havre Cedex, (Normandie) FranceIbn Zohr University, CST Campus Universitaire Ait Melloul Agadir, MoroccoIn this work, we consider the optimal harvesting and stability problems of a prey-predator model with modified Leslie-Gower and Holling-type II functional response. The model is governed by a system of three differential equations which describe the interactions between prey, predator and harvesting effort. Boundedness and existence of solutions for this system are showed. The existence and local stability of the possible steady states are analyzed and the conditions of global stability of the interior equilibrium are established by using the Lyapunov function, we prove also the occurrence of Hopf bifurcation at this point. By using the Pontryagin’s maximal principle, we formulate and we solve the problem of the optimal harvest policy. In the end, some numerical simulations are given to support our theoretical results.https://doi.org/10.1515/msds-2019-0001predator-prey modelordinary differential equationslocal and global stabilitybifurcationoptimal harvesting policy |
| spellingShingle | Abid W. Yafia R. Aziz-Alaoui M. A. Aghriche Ahmed Dynamics Analysis and Optimality in Selective Harvesting Predator-Prey Model With Modified Leslie-Gower and Holling-Type II Nonautonomous Dynamical Systems predator-prey model ordinary differential equations local and global stability bifurcation optimal harvesting policy |
| title | Dynamics Analysis and Optimality in Selective Harvesting Predator-Prey Model With Modified Leslie-Gower and Holling-Type II |
| title_full | Dynamics Analysis and Optimality in Selective Harvesting Predator-Prey Model With Modified Leslie-Gower and Holling-Type II |
| title_fullStr | Dynamics Analysis and Optimality in Selective Harvesting Predator-Prey Model With Modified Leslie-Gower and Holling-Type II |
| title_full_unstemmed | Dynamics Analysis and Optimality in Selective Harvesting Predator-Prey Model With Modified Leslie-Gower and Holling-Type II |
| title_short | Dynamics Analysis and Optimality in Selective Harvesting Predator-Prey Model With Modified Leslie-Gower and Holling-Type II |
| title_sort | dynamics analysis and optimality in selective harvesting predator prey model with modified leslie gower and holling type ii |
| topic | predator-prey model ordinary differential equations local and global stability bifurcation optimal harvesting policy |
| url | https://doi.org/10.1515/msds-2019-0001 |
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