Dynamic study of a predator-prey model with Allee effect and Holling type-I functional response

Abstract

In this paper, a prey-predator model with Allee effect and Holling type-I functional response is established, and its dynamical behaviors are studied in detail. The existence, boundedness and stability of the model are qualitatively discussed. Hopf bifurcation analysis is also taken into account. We further illustrate our theoretical analysis by means of numerical simulation. Using computer simulation, we found the position of each equilibrium point in the phase diagram that we drew. We found the threshold for undergoing a Hopf bifurcation in the bifurcation diagram. One of the interesting questions is which model with strong Allee effect is a bistable system.