Bifurcation in a Leslie–Gower system with fear in predators and strong Allee effect in prey

Abstract

In this paper, we consider a modified Leslie–Gower predator–prey model with Allee effect on prey and fear effect on predators. Results show complex dynamical behaviors in the model with these factors. Existence of equilibrium points and their stability of the model are first given. Then it is found that, with the Allee and fear effects, the model exhibits various and different bifurcations, such as saddle-node bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation. Theoretical analysis is verified through some numerical simulations.

Keywords

• fear effect
• Allee effect
• Hopf bifurcation
• Bogdanov–Takens bifurcation