Competitive exclusion and coexistence for competitive systems on ordered danach spaces

S. B. Hsu, Hal Smith, Paul Waltman

Research output: Contribution to journalArticle

117 Scopus citations

Abstract

The dynamics of competitive maps and semiflows defined on the product of two cones in respective Banach spaces is studied. It is shown that exactly one of three outcomes is possible for two viable competitors. Either one or the other population becomes extinct while the surviving population approaches a steady state, or there exists a positive steady state representing the coexistence of both populations.

Original languageEnglish (US)
Pages (from-to)4083-4094
Number of pages12
JournalTransactions of the American Mathematical Society
Volume348
Issue number10
StatePublished - Dec 1 1996

Keywords

  • Competitive systems
  • Discrete order-preserving semigroup
  • Ejective fixed points
  • Order-preserving semiflow
  • Positive fixed points

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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