Stationary patterns of a diffusive predator-prey model with Crowley-Martin functional response

•A diffusive predator-prey system with predator interference and Neumann boundary conditions is considered.•We show the existence and nonexistence of the nonconstant stationary solutions.•The methods used here can be applied to other predator-prey model with predator interference.

A diffusive predator-prey system with predator interference and Neumann boundary conditions is considered in this paper. We derive some results on the existence and nonexistence of nonconstant stationary solutions. It is shown that there exist no nonconstant stationary solutions when the effect of the predator interference is strong or the conversion rate of the predator is large, and nonconstant stationary solutions emerge when the diffusion rate of the predator is large.