Refuge used by prey as a function of predator numbers in a Leslie-type model
This paper deals with a continuous-time predator-prey model of Leslie-Gower type considering the use of a physical refuge by a fraction of the prey population. The fraction of hidden prey is assumed to be dependent on the presence of predators in the environment. The conditions for the existence of...
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| Format: | Article |
| Language: | Spanish |
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Universidad Nacional de Trujillo
2024-12-01
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| Series: | Selecciones Matemáticas |
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| Online Access: | https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6156 |
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| author | Paulo Tintinago-Ruiz Alejandro Rojas-Palma Eduardo González-Olivares |
| author_facet | Paulo Tintinago-Ruiz Alejandro Rojas-Palma Eduardo González-Olivares |
| author_sort | Paulo Tintinago-Ruiz |
| collection | DOAJ |
| description | This paper deals with a continuous-time predator-prey model of Leslie-Gower type considering the use of a physical refuge by a fraction of the prey population. The fraction of hidden prey is assumed to be dependent on the presence of predators in the environment.
The conditions for the existence of equilibrium points and their local stability are established.
In particular, it is shown that the point (0; 0) has a great importance in the dynamics of the model, since it determines a separating curve Σ that divides the behavior of the trajectories.
Those trajectories that are above this curve have as their w- limit the point (0; 0), so the extinction of both populations may be possible depending on the initial conditions. |
| format | Article |
| id | doaj-art-f5360520299544a7bb730ddf07b2d399 |
| institution | Kabale University |
| issn | 2411-1783 |
| language | Spanish |
| publishDate | 2024-12-01 |
| publisher | Universidad Nacional de Trujillo |
| record_format | Article |
| series | Selecciones Matemáticas |
| spelling | doaj-art-f5360520299544a7bb730ddf07b2d3992025-01-02T22:36:15ZspaUniversidad Nacional de TrujilloSelecciones Matemáticas2411-17832024-12-01110224925810.17268/sel.mat.2024.02.04Refuge used by prey as a function of predator numbers in a Leslie-type modelPaulo Tintinago-Ruiz0https://orcid.org/0000-0002-4100-2155Alejandro Rojas-Palma1https://orcid.org/0000-0002-5837-1571Eduardo González-Olivares2https://orcid.org/0000-0003-3907-0076Universidad del Quindío, Armenia, Colombia.Departamento de Matemática, Física y Estadística, Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca, ChilePontificia Universidad Católica de Valparaíso, ChileThis paper deals with a continuous-time predator-prey model of Leslie-Gower type considering the use of a physical refuge by a fraction of the prey population. The fraction of hidden prey is assumed to be dependent on the presence of predators in the environment. The conditions for the existence of equilibrium points and their local stability are established. In particular, it is shown that the point (0; 0) has a great importance in the dynamics of the model, since it determines a separating curve Σ that divides the behavior of the trajectories. Those trajectories that are above this curve have as their w- limit the point (0; 0), so the extinction of both populations may be possible depending on the initial conditions.https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6156predator-prey modelrefugestabilitybifurcationslimit cyclesseparatrix curves |
| spellingShingle | Paulo Tintinago-Ruiz Alejandro Rojas-Palma Eduardo González-Olivares Refuge used by prey as a function of predator numbers in a Leslie-type model Selecciones Matemáticas predator-prey model refuge stability bifurcations limit cycles separatrix curves |
| title | Refuge used by prey as a function of predator numbers in a Leslie-type model |
| title_full | Refuge used by prey as a function of predator numbers in a Leslie-type model |
| title_fullStr | Refuge used by prey as a function of predator numbers in a Leslie-type model |
| title_full_unstemmed | Refuge used by prey as a function of predator numbers in a Leslie-type model |
| title_short | Refuge used by prey as a function of predator numbers in a Leslie-type model |
| title_sort | refuge used by prey as a function of predator numbers in a leslie type model |
| topic | predator-prey model refuge stability bifurcations limit cycles separatrix curves |
| url | https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6156 |
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