A Leslie-Gower-type predation model considering generalist predators and the Allee effect on prey - Martínez-Jeraldo, Nicole (2021)
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.