Impact of the Allee Effect on the Dynamics of a Predator–Prey Model Exhibiting Group Defense
The Allee effect and group defense are two naturally occurring phenomena in the prey species of a predator–prey system. This research paper examines the impact of integrating the Allee effect on the dynamics of a predator–prey model, including a density-dependent functional response that reflects th...
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MDPI AG
2025-02-01
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| Series: | Mathematics |
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| author | Manoj Kumar Singh Arushi Sharma Luis M. Sánchez-Ruiz |
| author_facet | Manoj Kumar Singh Arushi Sharma Luis M. Sánchez-Ruiz |
| author_sort | Manoj Kumar Singh |
| collection | DOAJ |
| description | The Allee effect and group defense are two naturally occurring phenomena in the prey species of a predator–prey system. This research paper examines the impact of integrating the Allee effect on the dynamics of a predator–prey model, including a density-dependent functional response that reflects the defensive strategies of the prey population. Initially, the positivity and boundedness of the solutions are examined to ascertain the biological validity of the model. The presence of ecologically significant equilibrium points are established, followed by examining parametric restrictions for the local stability to comprehend the system dynamics in response to minor perturbations. A detailed computation encompasses diverse bifurcations, both of codimension one and two, which provide distinct dynamic behaviors of the model, such as oscillations, stable coexistence, and potential extinction scenarios. Numerical simulation has been provided to showcase complex dynamical behavior resulting from the Allee effect and prey group defense. |
| format | Article |
| id | doaj-art-88ed0172ea7844968b54085488a62fc0 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-88ed0172ea7844968b54085488a62fc02025-08-20T02:44:35ZengMDPI AGMathematics2227-73902025-02-0113463310.3390/math13040633Impact of the Allee Effect on the Dynamics of a Predator–Prey Model Exhibiting Group DefenseManoj Kumar Singh0Arushi Sharma1Luis M. Sánchez-Ruiz2Department of Mathematics and Statistics, Banasthali Vidyapith, Tonk 304022, IndiaDepartment of Mathematics and Statistics, Banasthali Vidyapith, Tonk 304022, IndiaDepartamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainThe Allee effect and group defense are two naturally occurring phenomena in the prey species of a predator–prey system. This research paper examines the impact of integrating the Allee effect on the dynamics of a predator–prey model, including a density-dependent functional response that reflects the defensive strategies of the prey population. Initially, the positivity and boundedness of the solutions are examined to ascertain the biological validity of the model. The presence of ecologically significant equilibrium points are established, followed by examining parametric restrictions for the local stability to comprehend the system dynamics in response to minor perturbations. A detailed computation encompasses diverse bifurcations, both of codimension one and two, which provide distinct dynamic behaviors of the model, such as oscillations, stable coexistence, and potential extinction scenarios. Numerical simulation has been provided to showcase complex dynamical behavior resulting from the Allee effect and prey group defense.https://www.mdpi.com/2227-7390/13/4/633predator–prey modelstabilitybifurcationmultiplicative Allee effectgroup defense |
| spellingShingle | Manoj Kumar Singh Arushi Sharma Luis M. Sánchez-Ruiz Impact of the Allee Effect on the Dynamics of a Predator–Prey Model Exhibiting Group Defense Mathematics predator–prey model stability bifurcation multiplicative Allee effect group defense |
| title | Impact of the Allee Effect on the Dynamics of a Predator–Prey Model Exhibiting Group Defense |
| title_full | Impact of the Allee Effect on the Dynamics of a Predator–Prey Model Exhibiting Group Defense |
| title_fullStr | Impact of the Allee Effect on the Dynamics of a Predator–Prey Model Exhibiting Group Defense |
| title_full_unstemmed | Impact of the Allee Effect on the Dynamics of a Predator–Prey Model Exhibiting Group Defense |
| title_short | Impact of the Allee Effect on the Dynamics of a Predator–Prey Model Exhibiting Group Defense |
| title_sort | impact of the allee effect on the dynamics of a predator prey model exhibiting group defense |
| topic | predator–prey model stability bifurcation multiplicative Allee effect group defense |
| url | https://www.mdpi.com/2227-7390/13/4/633 |
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