Periodic orbits of competitive and cooperative systems

Hal Smith

Research output: Contribution to journalArticle

49 Scopus citations

Abstract

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
Volume65
Issue number3
DOIs
StatePublished - Dec 1986

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Periodic orbits of competitive and cooperative systems'. Together they form a unique fingerprint.

  • Cite this