Qualitative Analysis of a Spatio-Temporal Leslie-Gower Predator-Prey Model with Weak Allee Effect and Nonlinear Harvesting

In the present paper, a predator-prey model with holling type IV functional response in the presence of weak Allee e ffect and non-linear harvesting in prey species has been proposed and analyzed. The local stability, existence of a Hopf bifurcation, direction of Hopf-bifurcation and the stability of the bifurcating periodic solution at the positive interior equilibrium point for the temporal model has been studied. The stability of positive constant equilibrium, Hopf-bifurcations, and di ffusion-driven Turing instability for the spatio-temporal model under the Neumann boundary conditions has also been analyzed. Numerical simulations have been carried out to validate the analytical findings.