The Poincare-Bendixson theorem for monotone cyclic feedback systems

John Mallet-Paret, Hal Smith

Research output: Contribution to journalArticlepeer-review

179 Scopus citations

Abstract

We prove the Poincare-Bendixson theorem for monotone cyclic feedback systems; that is, systems in Rn of the form {Mathematical expression} We apply our results to a variety of models of biological systems.

Original languageEnglish (US)
Pages (from-to)367-421
Number of pages55
JournalJournal of Dynamics and Differential Equations
Volume2
Issue number4
DOIs
StatePublished - Oct 1 1990

Keywords

  • Cellular control system
  • Poincare-Bendixson theorem
  • cyclic system
  • monotonicity
  • negative feedback

ASJC Scopus subject areas

  • Analysis

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