Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge
Fear and prey refuges are two significant topics in the ecological community because they are closely associated with the connectivity of natural resources. The effect of fear on prey populations and prey refuges (proportional to both the prey and predator) is investigated in the nonlinear-type pred...
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MDPI AG
2023-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/14/3118 |
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| author | Seralan Vinoth R. Vadivel Nien-Tsu Hu Chin-Sheng Chen Nallappan Gunasekaran |
| author_facet | Seralan Vinoth R. Vadivel Nien-Tsu Hu Chin-Sheng Chen Nallappan Gunasekaran |
| author_sort | Seralan Vinoth |
| collection | DOAJ |
| description | Fear and prey refuges are two significant topics in the ecological community because they are closely associated with the connectivity of natural resources. The effect of fear on prey populations and prey refuges (proportional to both the prey and predator) is investigated in the nonlinear-type predator-harvested Leslie–Gower model. This type of prey refuge is much more sensible and realistic than the constant prey refuge model. Because there is less research on the dynamics of this type of prey refuge, the current study has been considered to strengthen the existing literature. The number and stability properties of all positive equilibria are examined. Since the calculations for the determinant and trace of the Jacobian matrix are quite complicated at these equilibria, the stability of certain positive equilibria is evaluated using a numerical simulation process. Sotomayor’s theorem is used to derive a precise mathematical confirmation of the appearance of saddle-node bifurcation and transcritical bifurcation. Furthermore, numerical simulations are provided to visually demonstrate the dynamics of the system and the stability of the limit cycle is discussed with the help of the first Lyapunov number. We perform some sensitivity investigations on our model solutions in relation to three key model parameters: the fear impact, prey refuges, and harvesting. Our findings could facilitate some biological understanding of the interactions between predators and prey. |
| first_indexed | 2024-03-11T00:51:49Z |
| format | Article |
| id | doaj.art-73e76d0c798e4828abd8ac6669bfdfea |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T00:51:49Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-73e76d0c798e4828abd8ac6669bfdfea2023-11-18T20:20:49ZengMDPI AGMathematics2227-73902023-07-011114311810.3390/math11143118Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey RefugeSeralan Vinoth0R. Vadivel1Nien-Tsu Hu2Chin-Sheng Chen3Nallappan Gunasekaran4Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, IndiaDepartment of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket 83000, ThailandGraduate Institute of Automation Technology, National Taipei University of Technology, Taipei 10608, TaiwanGraduate Institute of Automation Technology, National Taipei University of Technology, Taipei 10608, TaiwanEastern Michigan Joint College of Engineering, Beibu Gulf University, Qinzhou 535011, ChinaFear and prey refuges are two significant topics in the ecological community because they are closely associated with the connectivity of natural resources. The effect of fear on prey populations and prey refuges (proportional to both the prey and predator) is investigated in the nonlinear-type predator-harvested Leslie–Gower model. This type of prey refuge is much more sensible and realistic than the constant prey refuge model. Because there is less research on the dynamics of this type of prey refuge, the current study has been considered to strengthen the existing literature. The number and stability properties of all positive equilibria are examined. Since the calculations for the determinant and trace of the Jacobian matrix are quite complicated at these equilibria, the stability of certain positive equilibria is evaluated using a numerical simulation process. Sotomayor’s theorem is used to derive a precise mathematical confirmation of the appearance of saddle-node bifurcation and transcritical bifurcation. Furthermore, numerical simulations are provided to visually demonstrate the dynamics of the system and the stability of the limit cycle is discussed with the help of the first Lyapunov number. We perform some sensitivity investigations on our model solutions in relation to three key model parameters: the fear impact, prey refuges, and harvesting. Our findings could facilitate some biological understanding of the interactions between predators and prey.https://www.mdpi.com/2227-7390/11/14/3118prey–predator interactionfear effectprey refugebifurcation analysis |
| spellingShingle | Seralan Vinoth R. Vadivel Nien-Tsu Hu Chin-Sheng Chen Nallappan Gunasekaran Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge Mathematics prey–predator interaction fear effect prey refuge bifurcation analysis |
| title | Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge |
| title_full | Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge |
| title_fullStr | Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge |
| title_full_unstemmed | Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge |
| title_short | Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge |
| title_sort | bifurcation analysis in a harvested modified leslie gower model incorporated with the fear factor and prey refuge |
| topic | prey–predator interaction fear effect prey refuge bifurcation analysis |
| url | https://www.mdpi.com/2227-7390/11/14/3118 |
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