Dynamics analysis of prey-predator model with allee effect and functional response

A prey-predator model with allee effect and functional response is established, which considers strong allee effect and weak alle effect on the prey-predator ecosystem. Boundedness and positiveness of solution of model system as well as existence of equilibria of model system is studied. By performing local stability analysis, locally asymptotical stability of model system around equilibria is investigated. Furthermore, a Lyapunov function is constructed to analyze the globally asymptotical stability of the proposed model system. Finally, numerical simulations are carried out to show efficiency of the theoretical analysis obtained in this paper.