Hopf bifurcation and stability analysis for a delayed prey-predator model subject to a strong Allee effect in the prey species

This study considers the linear stability of a prey-predator model including time delays under a strong Allee effect among prey species. We drive and analyze the corresponding characteristic transcendental equation, demonstrating the presence of Hopf bifurcation at the positive equilibrium point. We applied normal form approach and center manifold theorem to determine the Hopf bifurcation direction and the stability of the bifurcating periodic solution. A numerical example was ultimately introduced to demonstrate the effectiveness of the theoretical analysis.