We incorporate the strong Allee effect and fear effect in prey into a Leslie-Gower model. The origin is an attractor, which implies that the ecological system collapses at low densities. Qualitative analysis reveals that both effects are crucial in determining the dynamical behaviors of the model. There can be different types of bifurcations such as saddle-node bifurcation, non-degenerate Hopf bifurcation with a simple limit cycle, degenerate Hopf bifurcation with multiple limit cycles, Bogdanov-Takens bifurcation, and homoclinic bifurcation.
Keywords: Allee effect; Leslie-Gower model; bifurcation; fear effect; limit cycle.