Estabilidad en un modelo de depredación del tipo Leslie-Gower modificado considerando competencia entre los depredadores

• González-Olivares, Eduardo ^[1] ; Gallegos-Zuñiga, Javiera ^[1]
  1. [1] Pontificia Universidad Católica de Valparaíso

     Pontificia Universidad Católica de Valparaíso

     Valparaíso, Chile

     
• Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 7, Nº. 1, 2020 (Ejemplar dedicado a: January - July), págs. 10-24
• Idioma: español
• DOI: 10.17268/sel.mat.2020.01.02
• Títulos paralelos:
  • Stability in a modified Leslie-Gower type predation model considering competence among predators
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• Resumen
  • español

    En la literatura ecológica, la interferencia (autointerferencia) o competencia entre depredadores para realizar la captura de sus presas, ha sido modelada por diferentes formulaciones matemáticas. En este trabajo, estableceremos las propiedades dinámicas de modelos de depredación del tipo Leslie-Gower, en el que se incorpora una de estas formas, descrita por la función b (y) = yalfa, con 0 < alfa < 1.La principal dificultad del análisis se debe a que esta función no es diferenciable para y = 0, y la matriz Jacobiana no está definida en los puntos de equilibrio sobre el eje horizontal (eje x).Previamente mostramos un resumen con las propiedades fundamentales del modelo del tipo Leslie-Gower, con el objeto de efectuar un adecuado análisis comparativo con modelos donde se incorpora la auto-interferencia entre los depredadores.Para reforzar nuestros resultados se muestran algunas simulaciones numéricas.

  • English

    In the ecological literature, the interference (self-interference) or competition among predators to effect the harvesting of their prey has been modeled by different mathematical formulations.In this work, we will establish the dynamical properties of the Leslie-Gower type predation model, in which is incorporated one of these form, described by the function b (y) = yalfa , with 0 < alfa < 1.The main difficulty of the analysis is due to this function is not differentiable for y = 0, and the Jacobian matrix is not defined in the equilibrium points over the horizontal axis (x-axis).Previously, we showed a summary with the fundamental properties of the Leslie-Gower type model, in order to carry out an adequate comparative analysis with models where self-interference between predators is incorporated.To reinforce our results, some numerical simulations are shown.

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