Spatial Nonhomogeneous Periodic Solutions Induced by Nonlocal Prey Competition in a Diffusive Predator-Prey Model

The diffusive Holling-Tanner predator-prey model with no-flux boundary conditions and nonlocal prey competition is considered in this paper. We show the existence of spatially nonhomogeneous periodic solutions, which is induced by nonlocal prey competition. In particular, the constant positive steady state may lose the stability through Hopf bifurcation when the given parameter passes through some critical values, and the bifurcating periodic solutions near such values could be spatially nonhomogeneous and orbitally asymptotically stable.