A Leslie-Gower-type predation model considering generalist predators and the Allee effect on prey


  • 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.




Predator-prey model, bifurcation, limit cycles, separatrix curve, stability, functional response


The main feature of the Leslie-Gower-type predation model is that the predator’s growth function is one of logistic-type. Thus, it is a model assuming implicitly the competition among predators.

In this work the dynamics of a modified Leslie-Gower type predator-prey model is analyzed, considering two important aspects: (i) the predators capture an alternative food when the quantity of prey is scarce and (ii) the prey population is affected by an Allee effect.

Considering a topological equivalent system, the main properties of the system are established. Necessary and sufficient conditions for the existence and local stability of equilibria are determined, also showing the existence of a homoclinic orbit and of at least a limit cycle.

When the predators are generalists the dynamics of the model differ enough respecting the model considering predators specialist since appearing more equilibrium points and the mentioned homoclinic orbit.


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How to Cite

Martínez-Jeraldo, N., Rozas-Torres, E., & González-Olivares, E. (2021). A Leslie-Gower-type predation model considering generalist predators and the Allee effect on prey. Selecciones Matemáticas, 8(01), 147 - 160. https://doi.org/10.17268/sel.mat.2021.01.14