Periodic orbits of competitive and cooperative systems

Hal Smith

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


In this paper we consider the existence, location and stability type of periodic orbits of competitive and cooperative systems of autonomous ordinary differential equations. Particular attention is given to the existence of invariant manifolds related to periodic orbits and these results are used to improve a result of Hirsch for three dimensional irreducible competitive and cooperative systems. In particular, the Poincaré-Bendixson theorem holds for such three dimensional systems.

Original languageEnglish (US)
Pages (from-to)361-373
Number of pages13
JournalJournal of Differential Equations
Issue number3
StatePublished - Dec 1986

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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