A MODIFIED LESLIE-GOWER PREDATOR-PREY MODEL WITH HYPERBOLIC FUNCTIONAL RESPONSE AND ALLEE EFFECT ON PREY

摘要

This work deals with a modified Leslie-Gower type predator-prey model considering two important aspects for describe the interaction: the functional response is Hollling type II and the Allee effect acting in the prey growth function. With both assumptions, we have a modification of the known May-Holling-Tanner model, and the model obtained has a significative difference with those model due the existence of an equilibrium point over y-axis, which is an attractor for all parameter values. We prove the existence of separatrix curves on the phase plane dividing the behavior of the trajectories, which have different ω - limit. System has solutions highly sensitives to initial conditions To simplify the calculus we consider a topologically equivalent system with a minor quantity of parameters. For this new model, we prove that for certain subset of parameters, the model exhibits biestability phenomenon, since there exists an stable limit cycle surrounding a singularities of vector field or an stable positive equilibrium point.