Global dynamics of the smallest chemical reaction system with Hopf bifurcation

Hal Smith

doi:10.1007/s10910-011-9946-9

Global dynamics of the smallest chemical reaction system with Hopf bifurcation

Hal Smith

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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 language	English (US)
Pages (from-to)	989-995
Number of pages	7
Journal	Journal of Mathematical Chemistry
Volume	50
Issue number	4
DOIs	https://doi.org/10.1007/s10910-011-9946-9
State	Published - Apr 2012

Keywords

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

ASJC Scopus subject areas

General Chemistry
Applied Mathematics

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10.1007/s10910-011-9946-9

Cite this

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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",

note = "Funding Information: Hal L. Smith is supported by NSF Grant DMS-0918440.",

year = "2012",

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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

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DO - 10.1007/s10910-011-9946-9

M3 - Article

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EP - 995

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

IS - 4

ER -

Global dynamics of the smallest chemical reaction system with Hopf bifurcation

Abstract

Keywords

ASJC Scopus subject areas

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