The dynamics of a Leslie-Gower type tritrophic model are analyzed. The model considers the interaction among three populations, a resource, a predator and a superpredator. It is assumed that the predator is generalist and its interaction with the resource is according to a general Holling-type functional response. Furthermore, it is assumed that the superpredator is specialist and its interaction with the predator follows a Holling type II functional response. The goal of this work is to show conditions that guarantee the coexistence of the three species. To do this, the existence of a stable equilibrium point or a stable limit cycle is demonstrated, which appears via a bifurcation. In addition, the analytical results are exemplified through numerical simulations.
Keywords: 34C60; 37C75; 37G15; 92D25; Bautin bifurcation; Holling functional response; Hopf bifurcation; Leslie-Gower system; Tritrophic model.
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