Spreading speeds and traveling wavefronts for second order integrodifference equations

Abstract

This paper is concerned with the spreading speeds and traveling wavefronts for second order integrodifference equations. By introducing an auxiliary integrodifference system, the spreading speed is established for the integrodifference equation. It is shown that the spreading speed coincides with the minimal wave speed for monotonic traveling wavefronts. Furthermore, we prove that the traveling wavefronts are stable by applying the squeezing technique. Finally, we analyze the different effects of the delay term appearing in the integrodifference equation from the viewpoint of ecology.