Existence, uniqueness and asymptotic stability of time periodic traveling waves for a periodic Lotka-Volterra competition system with diffusion

Guangyu Zhao, Shigui Ruan

Research output: Contribution to journalArticle

53 Scopus citations

Abstract

We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a periodic diffusive Lotka-Volterra competition system. Under certain conditions, we prove that there exists a maximal wave speed c* such that for each wave speed c≤c*, there is a time periodic traveling wave connecting two semi-trivial periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co-moving frame coordinate. We also show that the traveling wave solutions with wave speed c<c* are asymptotically stable in certain sense. In addition, we establish the nonexistence of time periodic traveling waves for nonzero speed c>c*.

Original languageEnglish (US)
Pages (from-to)627-671
Number of pages45
JournalJournal des Mathematiques Pures et Appliquees
Volume95
Issue number6
DOIs
StatePublished - Jun 2011

Keywords

  • Asymptotic stability
  • Lotka-Volterra competition system
  • Maximal wave speed
  • Time periodic traveling wave

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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