Dynamics of a Leslie–Gower Model with Weak Allee Effect on Prey and Fear Effect on Predator

Abstract

In this paper, a Leslie–Gower model with weak Allee effect on prey and fear effect on predator is proposed. Compared with the case without fear effect on predator, the new model undergoes richer dynamic behaviors such as saddle-node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation. Also, different from the strong Allee effect on prey, the system with weak Allee effect has bistable attractors which are a largely stable limit cycle and a stable positive equilibrium, two stable equilibria, or a stable limit cycle and a stable trivial equilibrium. When the Allee effect coefficient is intermediate, fear effect on the predator can protect the prey and the predator from being extinguished. The results in this paper can be seen as a complement to those in the literatures about the Leslie–Gower model with Allee effect and fear effect.