Stability in a Holling-Tanner predator-prey model like a Kolmogorov system without periodic orbits via Dulac functions

Abstract

In this work, we find Dulac functions for Kolmogorov systems which can be applied to biological models in population. With a well choose of the Dulac function h we obtain stability and a phase diagram without periodic orbits. We prove that there are not periodic orbits at the interior of the first quadrant on the plane. We also obtain a generalized Kolmogorov system and apply this to the Holling-Tanner model and we use time series to understand its behaviour.