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January  2012, 17(1): 283-295. doi: 10.3934/dcdsb.2012.17.283

## A periodic reaction-diffusion model with a quiescent stage

 1 Department of Mathematics, National Tsing Hua University, Hsinchu 300, Taiwan

Received  June 2010 Revised  June 2011 Published  October 2011

In this paper, we investigate the asymptotic behaviour for a periodic reaction-diffusion model with a quiescent stage. By appealing to the theory of asymptotic speeds of spread and traveling waves for monotone periodic semiflow, we establish the existence of the spreading speed and show that it coincides with the minimal wave speed for monotone periodic traveling waves. Finally, we consider the case where the spatial domain is bounded. A threshold result on the global attractivity of either zero or a positive periodic solution are established.
Citation: Feng-Bin Wang. A periodic reaction-diffusion model with a quiescent stage. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 283-295. doi: 10.3934/dcdsb.2012.17.283
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