Traveling wave front for a two-component lattice dynamical system arising in competition models

Jong Shenq Guo*, Chang-Hong Wu

*Corresponding author for this work

Research output: Contribution to journalArticle

57 Scopus citations

Abstract

We study traveling front solutions for a two-component system on a one-dimensional lattice. This system arises in the study of the competition between two species with diffusion (or migration), if we divide the habitat into discrete regions or niches. We consider the case when the nonlinear source terms are of Lotka-Volterra type and of monostable case. We first show that there is a positive constant (the minimal wave speed) such that a traveling front exists if and only if its speed is above this minimal wave speed. Then we show that any wave profile is strictly monotone. Moreover, under some conditions, we show that the wave profile is unique (up to translations) for a given wave speed. Finally, we characterize the minimal wave speed by the parameters in the system.

Original languageEnglish
Pages (from-to)4357-4391
Number of pages35
JournalJournal of Differential Equations
Volume252
Issue number8
DOIs
StatePublished - 15 Apr 2012

Keywords

  • Competition model
  • Lattice dynamical system
  • Minimal wave speed
  • Monostable
  • Traveling front
  • Wave profile

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