Dynamics Analysis of Predator-Prey Model with Double Allee Effects and Holling Type II Functional Response

Abstract

In this article, a predator prey model with double Allee effects and Holling type II functional response is discussed. Strong and weak Allee effects were analyzed separately. The dynamic behavior of the model is analyzed by determining the equilibrium point and stability around the equilibrium point. From the analysis result, it is obtained that the trivial equilibrium point is locally asymptotically stable for the case of the strong Allee effect and the saddle unstable for the case of the weak Allee effect, while the boundary and coexistence equilibrium points are locally asymptotically stable if it satisfies several parameter conditions. Numerical simulations are carried out around the coexistence equilibrium point. The simulation results show that the Allee effect threshold affects prey population growth when experiencing a strong Allee effect. The growth of the prey population also depends on the initial conditions of the prey and predator population density. Furthermore, when the prey population experiences a weak Allee effect, there is no threshold must be exceeded for the population to survive so that for each initial condition however, the population will not experience extinction.