Convergence and Traveling Wave Solutions for a Predator-Prey System with Distributed Delays

This paper is concerned with the dynamics of a predator-prey system with distributed delays. The convergence of the corresponding functional differential system is proved by contracting rectangle, which also implies the convergence of the corresponding partial functional differential system when the spatial domain is smooth and the boundary condition is of Neumann. When the spatial domain is R, the minimal wave speed is obtained by presenting the existence and nonexistence of traveling wave solutions. It should be noted that this system does not satisfy comparison principle appealing to general predator-prey system due to time delay.