A Leslie-Gower-type predation model considering generalist predators and the Allee effect on prey
DOI:
https://doi.org/10.17268/sel.mat.2021.01.14Keywords:
Predator-prey model, bifurcation, limit cycles, separatrix curve, stability, functional responseAbstract
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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Copyright (c) 2021 Nicole Martínez-Jeraldo, Elizabeth Rozas-Torres, Eduardo González-Olivares
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