The Poincare-Bendixson theorem for monotone cyclic feedback systems

John Mallet-Paret, Hal Smith

Research output: Contribution to journalArticle

159 Citations (Scopus)

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 1990

Fingerprint

Poincaré-Bendixson Theorem
Feedback Systems
Biological Systems
Monotone
Model
Form

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

The Poincare-Bendixson theorem for monotone cyclic feedback systems. / Mallet-Paret, John; Smith, Hal.

In: Journal of Dynamics and Differential Equations, Vol. 2, No. 4, 10.1990, p. 367-421.

Research output: Contribution to journalArticle

@article{73b1e2ab1c674b848cded30b14305fb0,
title = "The Poincare-Bendixson theorem for monotone cyclic feedback systems",
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.",
keywords = "Cellular control system, cyclic system, monotonicity, negative feedback, Poincare-Bendixson theorem",
author = "John Mallet-Paret and Hal Smith",
year = "1990",
month = "10",
doi = "10.1007/BF01054041",
language = "English (US)",
volume = "2",
pages = "367--421",
journal = "Journal of Dynamics and Differential Equations",
issn = "1040-7294",
publisher = "Springer New York",
number = "4",

}

TY - JOUR

T1 - The Poincare-Bendixson theorem for monotone cyclic feedback systems

AU - Mallet-Paret, John

AU - Smith, Hal

PY - 1990/10

Y1 - 1990/10

N2 - 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.

AB - 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.

KW - Cellular control system

KW - cyclic system

KW - monotonicity

KW - negative feedback

KW - Poincare-Bendixson theorem

UR - http://www.scopus.com/inward/record.url?scp=0001051330&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001051330&partnerID=8YFLogxK

U2 - 10.1007/BF01054041

DO - 10.1007/BF01054041

M3 - Article

VL - 2

SP - 367

EP - 421

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

SN - 1040-7294

IS - 4

ER -