Global stability of traveling wavefronts for nonlocal reaction-diffusion equations with time delay

This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability of noncritical traveling wavefronts (waves with speeds c>c*, where c=c* is the minimal speed) is established, when the initial perturbations around the wavefront decays to zero exponentially in space as x→ − ∞, but it can be allowed arbitrary large in other locations, which improves the results in [9, 18, 21].