Abstract
In this paper, a diffusive predator–prey model with nonmonotonic functional response is investigated. The stability of the positive spatially homogeneous steady states and bifurcations of spatially homogeneous/nonhomogeneous time-periodic solutions as well as steady-state solutions are studied. In particular, the formulas determining the direction and the stability of the bifurcating periodic solutions are obtained. These results provide theoretical evidences to the complex spatiotemporal dynamics found by numerical simulations.