Existence and uniqueness of limit cycles in an enzyme-catalysed reaction system

F. A. Davidson; R. Xu; J. Liu

doi:10.1016/S0096-3003(01)00065-0

Existence and uniqueness of limit cycles in an enzyme-catalysed reaction system

F. A. Davidson (Lead / Corresponding author), R. Xu, J. Liu

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

14 Citations (Scopus)

Abstract

An enzyme-catalysed reaction system arising from glycolysis is investigated. By using the qualitative theory of ordinary differential equations, sufficient conditions are obtained for the existence, non-existence and uniqueness of limit cycles of the systems. Numerical continuation methods reveal the occurrence of large period solutions resulting from an almost homoclinic connection on a saddle point.

Original language	English
Pages (from-to)	165-179
Number of pages	15
Journal	Applied Mathematics and Computation
Volume	127
Issue number	2-3
DOIs	https://doi.org/10.1016/S0096-3003(01)00065-0
Publication status	Published - 15 Apr 2002

Keywords

Enzyme-catalysed
Global stability
Limit cycle

ASJC Scopus subject areas

Applied Mathematics
Computational Mathematics
Numerical Analysis

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10.1016/S0096-3003(01)00065-0

Cite this

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title = "Existence and uniqueness of limit cycles in an enzyme-catalysed reaction system",

abstract = "An enzyme-catalysed reaction system arising from glycolysis is investigated. By using the qualitative theory of ordinary differential equations, sufficient conditions are obtained for the existence, non-existence and uniqueness of limit cycles of the systems. Numerical continuation methods reveal the occurrence of large period solutions resulting from an almost homoclinic connection on a saddle point.",

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AU - Davidson, F. A.

AU - Xu, R.

AU - Liu, J.

PY - 2002/4/15

Y1 - 2002/4/15

N2 - An enzyme-catalysed reaction system arising from glycolysis is investigated. By using the qualitative theory of ordinary differential equations, sufficient conditions are obtained for the existence, non-existence and uniqueness of limit cycles of the systems. Numerical continuation methods reveal the occurrence of large period solutions resulting from an almost homoclinic connection on a saddle point.

AB - An enzyme-catalysed reaction system arising from glycolysis is investigated. By using the qualitative theory of ordinary differential equations, sufficient conditions are obtained for the existence, non-existence and uniqueness of limit cycles of the systems. Numerical continuation methods reveal the occurrence of large period solutions resulting from an almost homoclinic connection on a saddle point.

KW - Enzyme-catalysed

KW - Global stability

KW - Limit cycle

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U2 - 10.1016/S0096-3003(01)00065-0

DO - 10.1016/S0096-3003(01)00065-0

M3 - Article

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SN - 0096-3003

VL - 127

SP - 165

EP - 179

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2-3

ER -

Existence and uniqueness of limit cycles in an enzyme-catalysed reaction system

Abstract

Keywords

ASJC Scopus subject areas

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