Spreading speeds for the predator-prey system with nonlocal dispersal

In this paper, we mainly study the propagation properties of solutions of the predator-prey system with nonlocal dispersal. More specifically, we explored the spreading speeds of the predator and the prey in two different situations, namely, the predator spreads faster than the prey and the predator spreads slower than the prey. The main difficulty lies in the fact that the comparison principle cannot be used for the predator-prey system. We use the comparison principle of the scalar equation and the method of upper and lower solutions to prove the results. In addition, we establish the comparison principle of nonlocal dispersal equa-tions in space and time dependent environment. We conclude that the predator and the prey will eventually coexist by constructing a suitable Lyapunov functional. Finally, we use numerical simulations to illustrate the results. (c) 2022 Elsevier Inc. All rights reserved.