The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear
The avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying th...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/2112814 |
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| author | Firas Hussean Maghool Raid Kamel Naji |
| author_facet | Firas Hussean Maghool Raid Kamel Naji |
| author_sort | Firas Hussean Maghool |
| collection | DOAJ |
| description | The avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels. It is assumed that the generalist predator grows logistically using the Leslie-Gower type of growth function. All the solution properties of the model are studied. Local dynamics behaviors are investigated. The basin of attraction for each equilibrium is determined using the Lyapunov function. The conditions of persistence of the model are specified. The study of local bifurcation in the model is done. Numerical simulations are implemented to show the obtained results. It is watched that the system is wealthy in its dynamics including chaos. The fear factor works as a stabilizing factor in the system up to a specific level; otherwise, it leads to the extinction of the predator. However, increasing the prey’s group defense leads to extinction in predator species. |
| format | Article |
| id | doaj-art-bab0e09db8c54aa391b62aac07fddc09 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-bab0e09db8c54aa391b62aac07fddc092025-02-03T07:23:27ZengWileyJournal of Applied Mathematics1110-757X1687-00422021-01-01202110.1155/2021/21128142112814The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of FearFiras Hussean Maghool0Raid Kamel Naji1Department of Mathematics, College of Science, University of Baghdad, Baghdad, IraqDepartment of Mathematics, College of Science, University of Baghdad, Baghdad, IraqThe avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels. It is assumed that the generalist predator grows logistically using the Leslie-Gower type of growth function. All the solution properties of the model are studied. Local dynamics behaviors are investigated. The basin of attraction for each equilibrium is determined using the Lyapunov function. The conditions of persistence of the model are specified. The study of local bifurcation in the model is done. Numerical simulations are implemented to show the obtained results. It is watched that the system is wealthy in its dynamics including chaos. The fear factor works as a stabilizing factor in the system up to a specific level; otherwise, it leads to the extinction of the predator. However, increasing the prey’s group defense leads to extinction in predator species.http://dx.doi.org/10.1155/2021/2112814 |
| spellingShingle | Firas Hussean Maghool Raid Kamel Naji The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear Journal of Applied Mathematics |
| title | The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear |
| title_full | The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear |
| title_fullStr | The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear |
| title_full_unstemmed | The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear |
| title_short | The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear |
| title_sort | dynamics of a tritrophic leslie gower food web system with the effect of fear |
| url | http://dx.doi.org/10.1155/2021/2112814 |
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