Bifurcation analysis of a predator-prey model with strong Allee effect and Beddington-DeAngelis functional response

This manuscript examines the dynamics of a predator-prey model of the Beddington-DeAngelis type with strong Allee effect on prey growth function. Conditions for the existence and equilibria types are established. By taking Allee effect, predation rate of the prey and growth rate of the predator as bifurcation parameters, different potential bifurcations are explored, including codimension one bifurcations: fold bifurcation, transcritical bifurcation, Hopf bifurcation, and codimension two bifurcations: cusp bifurcation, Bogdanov-Takens bifurcation, and Bautin bifurcation. In addition, to confirm the dynamic behavior of the system, bifurcation diagrams are given in different parameter spaces and phase portraits are also presented to provide corresponding interpretation. The findings indicate that the dynamics of our system is much richer than the system with no strong Allee effect.