Rich Dynamics For A Classic Predator-prey Model With Weak Allee Effect

In this paper, the weak Allee effect on the predator is introduced into the classic predator-prey model of Lotka-Volterra type. Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. It is shown that the weak Allee effect can bring rich and complicated dynamics to the previously simple model, such as the saddle-node bifurcation, subcritical and supercritical Hopf bifurcations, and Bogdanov-Takcns bifurcations. These results reveal far richer dynamics compared to the model without Allee effect,implying that weak Allee effect can be one of the simple reasons for many complicated behaviors in the predator-prey communities.