Analysis of a Leslie-Gower predator-prey model with Allee effect and fear effect

Abstract: In this paper, the dynamical behaviors of a Leslie-Gower predator-prey model with Allee effect and fear effect are studied. First, we use Blow-Up method to explore the stability of the original point. Analyze the local stability of the non-negative equilibriums of the system. Taking the growth rate of predators as the Hopf bifurcation parameters. And give the condition of the model Hopf bifurcation. Using the method of calculating the first Lyapunov coefficient to discuss the direction of the Hopf bifurcation near the weak center.