Positive Solutions of a Predator-Prey Model with Additive Allee Effect

This paper deals with the positive solutions of a predator-prey model with additive Allee effect under Neumann boundary conditions. By applying the bifurcation theory, we provide a proof of the existence of local bifurcation solutions and describe the global behavior of these solutions. The result shows that the bifurcation curves can be extended infinitely along d(2) in the one-dimensional case. Moreover, the limiting behavior of the steady states is clarified using a shadow system approach. It appears that the shadow system exists with a positive solution and it can go into a terminal point when the parameter d(2) is sufficiently large.