On the number of limit cycles in a predator prey model with non-monotonic functional response

In this work we analyze a Gause type predator-prey model with a non-monotonic functional response and we show that it has two limit cycles encircling an unique singularity at the interior of the first quadrant, the innermost unstable and the outermost stable, completing the results obtained in previous paper [12, 17, 26, 28]. Moreover, using the Poisson bracket we give a proof, shorter than the ones found in the literature, for determining the type of a cusp point of a singularity at the first quadrant.