Dynamics in a diffusive predator-prey system with strong Allee effect and Ivlev-type functional response

The dynamics of a kind of reaction-diffusion predator-prey system with strong Allee effect in the prey population is considered. We prove the existence and uniqueness of the solution and give a priori bound. Hopf bifurcation and steady state bifurcation are studied. Results show that the Allee effect has significant impact on the dynamics.