Dynamics and pattern formation in diffusive predator-prey models with predator-taxis

Abstract

We consider a three-species predator-prey system in which the predator has a stage structure and the prey moves to avoid the mature predator, which is called the predator-taxis. We obtain the existence and uniform-in-time boundedness of classical global solutions for the model in any dimensional bounded domain with the Neumann boundary conditions. If the attractive predator-taxis coefficient is under a critical value, the homogenerous positive steady state maintains its stability. Otherwise, the system may generate Hopf bifurcation solutions. Our results suggest that the predator-taxis amplifies the spatial heterogeneity of the three-species predator-prey system, which is different from the effect of that in two-species predator-prey systems.