The dynamics of a Holling-Tanner predator-prey model with Allee effect

In this work, a modified Holling-Tanner predator-prey model with functional response Holling type II and Allee effect (strong and weak) is considered. It is shown that the dynamics is different to the original Holling-Tanner model, since new equilibrium points can appear in the first quadrant. In more detail, the modified model with strong Allee effect allows for the extinction of both species, while this is not possible in the other two models. In contrast, the modified model with strong Allee effect does not support stable limit cycles, while the other two models do. We also study the changes in the basins of attraction upon varying some of the system parameters. Computer simulations are also shown to illustrate the behaviour of the models.