Analysis of a discrete-time predator-prey system with Allee effect

This paper deals with a discrete-time predator-prey system with Allee effect. We obtain asymptotically stable conditions of the equilibrium points which are subject to the Allee effect. The stabilizing effect of Allee effect on prey and predator populations is studied, respectively. The Allee effect which occurs on both of predator and prey populations is also discussed by stability analysis, phase-plane and bifurcation diagram analysis. Our study suggests that Allee effect has stabilizing effect on population dynamics.