Dynamics of a time-periodic and delayed reaction-diffusion model with a quiescent stage

摘要

In this paper, we study a time-periodic and delayed reaction-diffusion system with quiescent stage in both unbounded and bounded habitat domains. In unbounded habitat domain $mathbb{R}$, we first prove the existence of the asymptotic spreading speed and then show that it coincides with the minimal wave speed for monotone periodic traveling waves. In a bounded habitat domain $Omegasubsetmathbb{R}^N (Ngeq1)$, we obtain the threshold result on the global attractivity of either the zero solution or the unique positive time-periodic solution of the system.