Spatial dynamics of a periodic population model with dispersal*

This paper is devoted to the study of spatial dynamics of a class of periodic integro-differential equations which describe the population dispersal process via a dispersal kernel. By appealing to the theory of asymptotic speeds of spread and travelling waves for monotonic periodic semiflows, we establish the existence of the spreading speed c * and the nonexistence of continuous periodic travelling wave solutions with wave speed c < c * . We also prove the existence of left-continuous periodic travelling waves with wave speed c ⩾ c * . In the autonomous case, the continuity of monotonic wave profiles with wave speed c ⩾ c * is obtained.