Dynamics and pattern formation in a diffusive predator–prey system with strong Allee effect in prey

The dynamics of a reaction–diffusion predator–prey system with strong Allee effect in the prey population is considered. Nonexistence of nonconstant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation. Bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as nonconstant steady state solutions are studied. These results show that the impact of the Allee effect essentially increases the system spatiotemporal complexity.