Global dynamics of the smallest chemical reaction system with Hopf bifurcation

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The global behavior of solutions is described for the smallest chemical reaction system that exhibits a Hopf bifurcation, discovered in [12]. This three-dimensional system is a competitive system and a monotone cyclic feedback system. The Poincaré-Bendixson theory extends to such systems [2,3,6,8] and a Bendixson criterion exists to rule out periodic orbits [4].

Original languageEnglish (US)
Pages (from-to)989-995
Number of pages7
JournalJournal of Mathematical Chemistry
Volume50
Issue number4
DOIs
StatePublished - Apr 2012

Fingerprint

Hopf bifurcation
Global Dynamics
Chemical Reaction
Hopf Bifurcation
Chemical reactions
Orbits
Feedback
Competitive System
Feedback Systems
Behavior of Solutions
Periodic Orbits
Monotone
Three-dimensional

Keywords

  • Bendixson criterion
  • Compact attractor
  • Competitive system
  • Monotone cyclic feedback system
  • Periodic orbit
  • Uniform persistence

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

Cite this

Global dynamics of the smallest chemical reaction system with Hopf bifurcation. / Smith, Hal.

In: Journal of Mathematical Chemistry, Vol. 50, No. 4, 04.2012, p. 989-995.

Research output: Contribution to journalArticle

@article{5348336917a941269292a1a7226e8769,
title = "Global dynamics of the smallest chemical reaction system with Hopf bifurcation",
abstract = "The global behavior of solutions is described for the smallest chemical reaction system that exhibits a Hopf bifurcation, discovered in [12]. This three-dimensional system is a competitive system and a monotone cyclic feedback system. The Poincar{\'e}-Bendixson theory extends to such systems [2,3,6,8] and a Bendixson criterion exists to rule out periodic orbits [4].",
keywords = "Bendixson criterion, Compact attractor, Competitive system, Monotone cyclic feedback system, Periodic orbit, Uniform persistence",
author = "Hal Smith",
year = "2012",
month = "4",
doi = "10.1007/s10910-011-9946-9",
language = "English (US)",
volume = "50",
pages = "989--995",
journal = "Journal of Mathematical Chemistry",
issn = "0259-9791",
publisher = "Springer Netherlands",
number = "4",

}

TY - JOUR

T1 - Global dynamics of the smallest chemical reaction system with Hopf bifurcation

AU - Smith, Hal

PY - 2012/4

Y1 - 2012/4

N2 - The global behavior of solutions is described for the smallest chemical reaction system that exhibits a Hopf bifurcation, discovered in [12]. This three-dimensional system is a competitive system and a monotone cyclic feedback system. The Poincaré-Bendixson theory extends to such systems [2,3,6,8] and a Bendixson criterion exists to rule out periodic orbits [4].

AB - The global behavior of solutions is described for the smallest chemical reaction system that exhibits a Hopf bifurcation, discovered in [12]. This three-dimensional system is a competitive system and a monotone cyclic feedback system. The Poincaré-Bendixson theory extends to such systems [2,3,6,8] and a Bendixson criterion exists to rule out periodic orbits [4].

KW - Bendixson criterion

KW - Compact attractor

KW - Competitive system

KW - Monotone cyclic feedback system

KW - Periodic orbit

KW - Uniform persistence

UR - http://www.scopus.com/inward/record.url?scp=84857996699&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857996699&partnerID=8YFLogxK

U2 - 10.1007/s10910-011-9946-9

DO - 10.1007/s10910-011-9946-9

M3 - Article

AN - SCOPUS:84857996699

VL - 50

SP - 989

EP - 995

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

SN - 0259-9791

IS - 4

ER -