Traveling waves in delayed predator–prey systems with nonlocal diffusion and stage structure

This paper is concerned with the existence of traveling wave solutions of a delayed predator–prey system with stage structure and nonlocal diffusion. By introducing the partial quasi-monotone condition and cross-iteration scheme, we first consider a class of delayed systems with nonlocal diffusion and deduce the existence of traveling wave solutions to the existence of a pair of upper–lower solutions. When the result is applied to the predator–prey system, we establish the existence of traveling wave solutions, as well as its precisely asymptotic behavior. Our result implies that there is a transition zone moving from the steady state with no species to the steady state with the coexistence of both species.