Abstract

This work deals with a modified Leslie-Gower–type model, in which two ecolog-ical issues are considered. (i) The action of predators over their prey is describedby a nonmonotonic functional response, and (ii) the predators are general-ists, ie, in absence of their favorite prey, they look for an alternative food. Theproposed model is described by an autonomous differential equation systemof Kolmogorov type, which has interesting and rich dynamics. We extend theresults obtained in previous research articles, where the predators are consideredspecialists. It is shown that the model can have up to three positive equilibriacoexisting for a wide set of parameters, one of them being a saddle point and theother can be a focus of multiplicity two. Moreover, these points can coincide toobtain a codimension-two cusp point. Varying the parameters in a small neigh-borhood of the parameter values, the model undergoes the Bogdanov-Takensbifurcation and a multiple Hopf bifurcation in the vicinities of these two equi-libria, respectively. To reinforce our analytical results, numerical simulationsare shown. Furthermore, graphical simulations of some properties that did notprove in the text were also added.