Spreading speeds and traveling waves in competitive recursion systems

Guo Lin, Wan Tong Li, Shigui Ruan

Research output: Contribution to journalArticle

29 Scopus citations

Abstract

This paper is concerned with the spreading speeds and traveling wave solutions of discrete time recursion systems, which describe the spatial propagation mode of two competitive invaders. We first establish the existence of traveling wave solutions when the wave speed is larger than a given threshold. Furthermore, we prove that the threshold is the spreading speed of one species while the spreading speed of the other species is distinctly slower compared to the case when the interspecific competition disappears. Our results also show that the interspecific competition does affect the spread of both species so that the eventual population densities at the coexistence domain are lower than the case when the competition vanishes.

Original languageEnglish (US)
Pages (from-to)165-201
Number of pages37
JournalJournal of Mathematical Biology
Volume62
Issue number2
DOIs
StatePublished - Feb 1 2011

Keywords

  • Comparison principle
  • Competitive invaders
  • Spreading speeds
  • Traveling waves
  • Upper and lower solutions

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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