Stable periodic solutions for the hypercycle system

J. Hofbauer; J. Mallet-Paret; Hal Smith

doi:10.1007/BF01049740

Stable periodic solutions for the hypercycle system

J. Hofbauer, J. Mallet-Paret, Hal Smith

Mathematical and Statistical Sciences, School of (SoMSS)

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

38 Scopus citations

Abstract

We consider the hypercycle system of ODEs, which models the concentration of a set of polynucleotides in a flow reactor. Under general conditions, we prove the omega-limit set of any orbit is either an equilibrium or a periodic orbit. The existence of an orbitally asymptotic stable periodic orbit is shown for a broad class of such systems.

Original language	English (US)
Pages (from-to)	423-436
Number of pages	14
Journal	Journal of Dynamics and Differential Equations
Volume	3
Issue number	3
DOIs	https://doi.org/10.1007/BF01049740
State	Published - Jul 1991

Keywords

Competitive systems
Poincaré-Bendixson
cyclic systems
hypercycle system
monotonicity

ASJC Scopus subject areas

Analysis

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10.1007/BF01049740

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abstract = "We consider the hypercycle system of ODEs, which models the concentration of a set of polynucleotides in a flow reactor. Under general conditions, we prove the omega-limit set of any orbit is either an equilibrium or a periodic orbit. The existence of an orbitally asymptotic stable periodic orbit is shown for a broad class of such systems.",

keywords = "Competitive systems, Poincar{\'e}-Bendixson, cyclic systems, hypercycle system, monotonicity",

author = "J. Hofbauer and J. Mallet-Paret and Hal Smith",

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AU - Mallet-Paret, J.

AU - Smith, Hal

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N2 - We consider the hypercycle system of ODEs, which models the concentration of a set of polynucleotides in a flow reactor. Under general conditions, we prove the omega-limit set of any orbit is either an equilibrium or a periodic orbit. The existence of an orbitally asymptotic stable periodic orbit is shown for a broad class of such systems.

AB - We consider the hypercycle system of ODEs, which models the concentration of a set of polynucleotides in a flow reactor. Under general conditions, we prove the omega-limit set of any orbit is either an equilibrium or a periodic orbit. The existence of an orbitally asymptotic stable periodic orbit is shown for a broad class of such systems.

KW - Competitive systems

KW - Poincaré-Bendixson

KW - cyclic systems

KW - hypercycle system

KW - monotonicity

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JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

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ER -

Stable periodic solutions for the hypercycle system

Abstract

Keywords

ASJC Scopus subject areas

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