Traveling Fronts for a Time-periodic Population Model with Dispersal

In this paper, we study a class of time-periodic population model with dispersal. It is well known that the existence of the periodic traveling fronts has been established. However, the uniqueness and stability of such fronts remain unsolved. In this paper, we first prove the uniqueness of non-critical periodic traveling fronts. Then, we show that all non-critical periodic traveling fronts are exponentially asymptotically stable.