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

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...

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Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations 2016-01, Vol.2016 (47), p.1-25
Main Authors: Wang, Shuang-Ming, Zhang, Liang
Format: Article
Language:English
Subjects:
delay
global attractivity
quiescent stage
spreading speed
time-periodic
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Summary: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 $\Omega\subset\mathbb{R}^N\ (N\geq1)$, we obtain the threshold result on the global attractivity of either the zero solution or the unique positive time-periodic solution of the system.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2016.1.47