Consequences of Weak Allee Effect in a Leslie–Gower-Type Predator–Prey Model with a Generalized Holling Type III Functional Response

In this work, we analyze a predator–prey model derived from the Leslie–Gower type model considering two modifications: a generalized Holling type III functional response and a weak Allee 430054755 effect on prey, which is described by an autonomous bidimensional ordinary differential equation system. Conditions for the existence of the equilibrium points or singularities and their nature are determined. The existence of separatrix curves on the phase plane dividing the behavior of the trajectories are also shown. Thus, two closed solutions but in different sides of this separatrix curve can have different ω-limit sets; therefore, there exist trajectories highly sensitive to initial conditions. The existence of constraints on the parameter values for which the unique equilibrium point at the first quadrant is unstable and surrounded by a unique limit cycle in the phase plane is also proven. Computer simulations are also given in order to support our conclusions.