Propagation direction of bistable pulsating waves for a nonlocal and delayed population model in discrete periodic habitat

How does spatio-temporal heterogeneity influence the propagation direction of bistable waves? To explore this question we formulate a nonlocal and time-delay population model with directional dispersal in discrete periodic habitat. Within a bistability framework, we determine the speed sign of bistable pulsating wave, followed by the existence and uniqueness of the pulsating wave. It turns out that time delay does not influence the sign but spatial heterogeneity does. Furthermore, dispersal strategies that ensure propagation success are shown to exist.