Double Hopf bifurcation of a diffusive predator–prey system with strong Allee effect and two delays

In this paper, we consider a diffusive predator–prey system with strong Allee effect and two delays. First, explore the stability region of positive constant steady state by calculating switching curves. Then derive Hopf double bifurcation theorem via crossing directions Moreover, calculate normal forms near singularities taking delays as parameters. We carry out some numerical simulations for illustrating theoretical results. Both analysis simulation show that singularity has rich dynamics, including stable spatially homogeneous inhomogeneous periodic solutions. Finally, evaluate influence parameters on existence bifurcation.