DYNAMICS OF A SIMPLIFIED HOLLING IV TYPE PREDATOR–PREY SYSTEM WITH WEAK ALLEE EFFECT ON PREY AND ANTI-PREDATOR BEHAVIOR

In this paper, we investigate a simplified Holling IV type predator–prey model with weak Allee effect on prey and anti-predator behavior. First, the existence and stability of all possible equilibria are analyzed, which suggests the changing trend of the predator-prey system under different initial values. Second, bifurcation analysis at the equilibria are performed to explore the dynamic behavior of the system while the parameters pass the critical values, which reveals the influence of the death rate, anti-predator behavior and weak Allee effect on the system. It is found that the system undergoes saddle-node bifurcation, cusp type Bogdanov–Takens bifurcation of codimension 2 and 3, and Hopf bifurcation, forming the organizing center of a series of codimensional bifurcations. The bifurcations indicate the change of the final state and the occurrence of oscillations of the predator–prey system under different parameters. Finally, the theoretical results are confirmed by numerical simulations.