Bifurcations on a discontinuous Leslie–Grower model with harvesting and alternative food for predators and Holling II functional response

Abstract

This paper proposes a mathematical model that describes the interaction of prey and predators, assuming logistic growth for both species, harvesting and alternative food for predators and functional response of the Holling II predator. When performing a qualitative analysis to determine conditions in the parameters that allow the possible extinction or preservation of prey and/or predators, a modification of the initial model is made considering that the consumption of prey by predators is restricted if the amount of prey is less than a critical value, whose dynamics is formulated by a planar Filippov system. The study of the discontinuous model is carried out by bifurcation analysis in relation to two parameters: harvesting of predators and critical value of prey.