Global attractivity, spreading speeds and traveling waves of delayed nonlocal reaction-diffusion systems

Shi Liang Wu, Cheng Hsiung Hsu, Yanyu Xiao

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

The purpose of this work is to study the spatial dynamics of some delayed nonlocal reaction-diffusion systems in whole space. We first establish a series of comparison theorems to investigate the global attractivity of the equilibria for a delayed nonlocal reaction-diffusion system with and without quasi-monotonicity. Then we show that the spreading speed of a general system without quasi-monotone conditions is coincident with the minimal wave speed. Applying a fluctuation method, we further provide some sufficient conditions to ensure the upward convergence of the spreading speed and traveling wave solutions. Finally, we point out the effects of the delay and nonlocality on the spreading speed of the non-quasi-monotone systems.

Original languageEnglish
Pages (from-to)1058-1105
Number of pages48
JournalJournal of Differential Equations
Volume258
Issue number4
DOIs
StatePublished - 15 Feb 2015

Keywords

  • Global attractivity
  • Minimal wave speed
  • Spreading speed
  • Time delay and nonlocality
  • Traveling wave solution

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