Propagation dynamics in a non-local dispersal system with shifting habitats

Abstract This paper is concerned with the propagation dynamics of a general non-local dispersal system with shifting habitats. By constructing appropriate upper and lower solutions, and applying the fixed-point theory, we prove the existence of a non-decreasing wave front with speed consistent with the habitat shifting speed. Moreover, using the sliding method, the uniqueness of forced waves is obtained. And, the stability of the forced waves is proved by applying the dynamical systems approach. Finally, we give an application and the corresponding numerical simulation to illustrate our analytical results.