Wave propagation for a two-component lattice dynamical system arising in strong competition models

Jong Shenq Guo*, Chang-Hong Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

We study a Lotka-Volterra type competition system with bistable nonlinearity in which the habitat is divided into discrete niches. We show that there exist non-monotone stationary solutions when the migration coefficients are sufficiently small. Also, we prove that the propagation failure phenomenon occurs. Finally, we focus on the traveling wave with nonzero wave speed. By investigating the asymptotic behavior of tails of wave profiles, we show that nonzero speed wave profiles are monotone. Moreover, the nonzero wave speed is unique in the sense that the wave cannot propagate with two different nonzero wave speeds.

Original languageEnglish
Pages (from-to)3504-3533
Number of pages30
JournalJournal of Differential Equations
Volume250
Issue number8
DOIs
StatePublished - 15 Apr 2011

Keywords

  • Lattice dynamical system
  • Propagation failure
  • Stationary solution
  • Traveling wave
  • Wave speed

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