Observations of a torus in a model of the Belousov-Zhabotinskii reaction

Dwight Barkley; John Ringland; Jack S. Turner

doi:10.1063/1.452937

Observations of a torus in a model of the Belousov-Zhabotinskii reaction

Dwight Barkley
, John Ringland
, Jack S. Turner

Mathematics

University of Texas at Austin

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

34 Scopus citations

Abstract

The first observation of quasiperiodic oscillations in a model of the Belousov-Zhabotinskii reaction is presented and the evolution along two parameter paths of the associated torus is described. Comparison is made with experiment and the hysteresis-Hopf normal form. The model dynamics is shown to be more complex than that of the normal form. The torus is also shown to be related to two other features of the BZ reaction: (1) the transition from small amplitude to mixed-mode oscillations and (2) alternating periodic-chaotic sequences.

Original language	English
Pages (from-to)	3812-3820
Number of pages	9
Journal	Journal of Chemical Physics
Volume	87
Issue number	7
DOIs	https://doi.org/10.1063/1.452937
State	Published - 1987

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title = "Observations of a torus in a model of the Belousov-Zhabotinskii reaction",

abstract = "The first observation of quasiperiodic oscillations in a model of the Belousov-Zhabotinskii reaction is presented and the evolution along two parameter paths of the associated torus is described. Comparison is made with experiment and the hysteresis-Hopf normal form. The model dynamics is shown to be more complex than that of the normal form. The torus is also shown to be related to two other features of the BZ reaction: (1) the transition from small amplitude to mixed-mode oscillations and (2) alternating periodic-chaotic sequences.",

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AU - Barkley, Dwight

AU - Ringland, John

AU - Turner, Jack S.

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N2 - The first observation of quasiperiodic oscillations in a model of the Belousov-Zhabotinskii reaction is presented and the evolution along two parameter paths of the associated torus is described. Comparison is made with experiment and the hysteresis-Hopf normal form. The model dynamics is shown to be more complex than that of the normal form. The torus is also shown to be related to two other features of the BZ reaction: (1) the transition from small amplitude to mixed-mode oscillations and (2) alternating periodic-chaotic sequences.

AB - The first observation of quasiperiodic oscillations in a model of the Belousov-Zhabotinskii reaction is presented and the evolution along two parameter paths of the associated torus is described. Comparison is made with experiment and the hysteresis-Hopf normal form. The model dynamics is shown to be more complex than that of the normal form. The torus is also shown to be related to two other features of the BZ reaction: (1) the transition from small amplitude to mixed-mode oscillations and (2) alternating periodic-chaotic sequences.

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U2 - 10.1063/1.452937

DO - 10.1063/1.452937

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EP - 3820

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

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ER -

Observations of a torus in a model of the Belousov-Zhabotinskii reaction

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