Stable coexistence and bi-stability for competitive systems on ordered Banach spaces

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30 Scopus citations


Autonomous and asymptotically autonomous semiflows modeling two species competition are studied which are strongly order preserving on a convex subset of a Banach space with competitive order. Conditions are derived for stable coexistence, bi-stability, and competitive exclusion. A complete classification of all possible outcomes is obtained in case that there is at most one positive steady state representing coexistence of both species.

Original languageEnglish (US)
Pages (from-to)195-222
Number of pages28
JournalJournal of Differential Equations
Issue number1
StatePublished - Oct 10 2001



  • Asymptotically autonomous semiflows
  • Competitive systems
  • Order-preserving semiflows
  • Positive fixed points

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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