  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.
