Analysis of a May-Holling-Tanner rate-dependent predator-prey model with an alternative food source for the predator with a weak Allee effect for the prey

In this study, a May-Holling-Tanner-type mathematical model of the predator-prey interaction is analyzed, incorporating an alternative food source for the predator and a weak Allee effect on the prey population. The model is described using a two-dimensional system of ordinary differential equations. The existence, uniqueness, and positivity of the solutions were investigated, ensuring that the populations were maintained at biologically meaningful values. Furthermore, local and global stability conditions at critical points suitable for ecological equilibrium are explored using tools such as the generalized Krasovskii theorem. Likewise, the existence of periodic solutions in certain scenarios is based on the Dulac criterion. Finally, a numerical analysis using Python simulations is performed to corroborate the theoretical results, highlighting the asymptotic stability of the populations under certain initial and parameter conditions.