Un modelo de depredación del tipo Leslie-Gower considerando depredadores generalistas y efecto Allee en las presas

Autores/as

  • Nicole Martínez-Jeraldo Doctorado Modelamiento Matemático Aplicado, Universidad Católica del Maule, Talca, Chile.
  • Elizabeth Rozas-Torres Centro Docencia de Ciencias Básicas para Ing. Universidad Austral de Chile, Valdivia, Chile.
  • Eduardo González-Olivares Pontificia Universidad Católica de Valparaíso, Chile.

DOI:

https://doi.org/10.17268/sel.mat.2021.01.14

Palabras clave:

Modelo depredador-presa, bifurcación, ciclo límite, curva separatriz, estabilidad, respuesta funcional

Resumen

La característica principal de los modelos del tipo Leslie-Gower, es que la ecuación de crecimiento de los depredadores es descrita por la función de logística. Por lo tanto, es un modelo que supone implícitamente la competencia entre los depredadores.

En este trabajo se analiza la dinámica de un modelo derivado del modelo de Leslie-Gower,considerando dos aspectos importantes: (i) los depredadores capturan un alimento alternativo cuando la cantidad de presas es escasa y (ii) la población de presas se ve afectada por un efecto Allee.

Considerando un sistema equivalente topológico, se establecen las principales propiedades del modelo. Se determinan las condiciones necesarias y suficientes para la existencia y la estabilidad local de los equilibrios. Además, se prueba la existencia de una órbita homoclínica y de al menos un ciclo límite.

Cuando los depredadores son generalistas, la dinámica del modelo difiere bastante con respecto al modelo donde los depredadores son especialistas. Dinámicamente aparecen más puntos de equilibrio y una órbita homoclínica.

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Publicado

2021-07-29

Cómo citar

Martínez-Jeraldo, N., Rozas-Torres, E., & González-Olivares, E. (2021). Un modelo de depredación del tipo Leslie-Gower considerando depredadores generalistas y efecto Allee en las presas. Selecciones Matemáticas, 8(01), 147 - 160. https://doi.org/10.17268/sel.mat.2021.01.14

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