Spatial patterns in a diffusive Holling--Tanner predator-prey model with weak Allee effect on the prey

In this work, we consider temporal and spatio-temporal Holling--Tanner predator-prey models with Holling type II functional response and weak Allee effect on the prey. We show that the model has at most three equilibrium points in the first quadrant, one is always a saddle point while the other two can be a repeller and/or an attractor. From our results of the temporal model, we identify regions in parameter space in which Turing instabilities in the spatio-temporal model are expected for two of the equilibrium points. Subsequently, we analyse these instabilities. We use simulations to illustrate the behaviour of both the temporal and spatio-temporal