Periodic orbits of competitive and cooperative systems

Research output: Contribution to journalArticle

48 Citations (Scopus)

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 - 1986

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Competitive System
Cooperative Systems
Periodic Orbits
Orbits
Three-dimensional
Invariant Manifolds
Ordinary differential equations
Ordinary differential equation
Theorem

ASJC Scopus subject areas

  • Analysis

Cite this

Periodic orbits of competitive and cooperative systems. / Smith, Hal.

In: Journal of Differential Equations, Vol. 65, No. 3, 1986, p. 361-373.

Research output: Contribution to journalArticle

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