Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model
In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consum...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2021/1366797 |
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| author | Noor S. Sh. Barhoom Sadiq Al-Nassir |
| author_facet | Noor S. Sh. Barhoom Sadiq Al-Nassir |
| author_sort | Noor S. Sh. Barhoom |
| collection | DOAJ |
| description | In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynamics of our proposed model. |
| format | Article |
| id | doaj-art-f0e05d027ccc4086899bc974abbd6fc7 |
| institution | Kabale University |
| issn | 1687-0409 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f0e05d027ccc4086899bc974abbd6fc72025-02-03T07:24:15ZengWileyAbstract and Applied Analysis1687-04092021-01-01202110.1155/2021/1366797Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator ModelNoor S. Sh. Barhoom0Sadiq Al-Nassir1Department of MathematicsDepartment of MathematicsIn this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynamics of our proposed model.http://dx.doi.org/10.1155/2021/1366797 |
| spellingShingle | Noor S. Sh. Barhoom Sadiq Al-Nassir Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model Abstract and Applied Analysis |
| title | Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model |
| title_full | Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model |
| title_fullStr | Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model |
| title_full_unstemmed | Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model |
| title_short | Dynamical Behaviors of a Fractional-Order Three Dimensional Prey-Predator Model |
| title_sort | dynamical behaviors of a fractional order three dimensional prey predator model |
| url | http://dx.doi.org/10.1155/2021/1366797 |
| work_keys_str_mv | AT noorsshbarhoom dynamicalbehaviorsofafractionalorderthreedimensionalpreypredatormodel AT sadiqalnassir dynamicalbehaviorsofafractionalorderthreedimensionalpreypredatormodel |