On a predator-prey reaction-diffusion model with nonlocal effects

•A predator-prey system with integral term is considered.•The properties of the solution of the initial problem are investigated.•The comparison principle is established and monotone sequence are constructed.•The conditions of occurring Turing bifurcation are given and numerical simulations are carried out to illustrate it. In this paper, we consider an initial value problem of a predator-prey system with integral term. By establishing comparison principle and constructing monotone sequences, the existence and uniqueness for the solution of that problem is proved. Then we further show the uniform boundedness. Finally, some conditions of Turing bifurcation occurring are given and illustrated by numerical simulations.