Bifurcation from excitability to limit cycle oscillations at the end of the induction period in the classical Belousov-Zhabotinsky reaction

Z. Noszticzius, M. Wittmann, Peter Stirling

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Abstract

The appearance of full blown oscillations at the end of the induction period in the classical BZ reaction (substrate: malonic acid) is usually explained by a subcritical Hopf bifurcation. Our perturbation experiments have revealed that the classical BZ reaction is excitable in its induction period and the threshold of excitability is decreasing gradually to zero during that period. Thus the sudden appearance of limit cycle oscillations at the end of the induction period can be explained by a saddle-node infinite period (SNIPER) bifurcation as well.

Original languageEnglish
Pages (from-to)1922-1926
Number of pages5
JournalThe Journal of Chemical Physics
Volume86
Issue number4
Publication statusPublished - 1986

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Hopf bifurcation
induction
oscillations
cycles
Substrates
Experiments
saddles
perturbation
acids
thresholds
malonic acid

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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abstract = "The appearance of full blown oscillations at the end of the induction period in the classical BZ reaction (substrate: malonic acid) is usually explained by a subcritical Hopf bifurcation. Our perturbation experiments have revealed that the classical BZ reaction is excitable in its induction period and the threshold of excitability is decreasing gradually to zero during that period. Thus the sudden appearance of limit cycle oscillations at the end of the induction period can be explained by a saddle-node infinite period (SNIPER) bifurcation as well.",
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N2 - The appearance of full blown oscillations at the end of the induction period in the classical BZ reaction (substrate: malonic acid) is usually explained by a subcritical Hopf bifurcation. Our perturbation experiments have revealed that the classical BZ reaction is excitable in its induction period and the threshold of excitability is decreasing gradually to zero during that period. Thus the sudden appearance of limit cycle oscillations at the end of the induction period can be explained by a saddle-node infinite period (SNIPER) bifurcation as well.

AB - The appearance of full blown oscillations at the end of the induction period in the classical BZ reaction (substrate: malonic acid) is usually explained by a subcritical Hopf bifurcation. Our perturbation experiments have revealed that the classical BZ reaction is excitable in its induction period and the threshold of excitability is decreasing gradually to zero during that period. Thus the sudden appearance of limit cycle oscillations at the end of the induction period can be explained by a saddle-node infinite period (SNIPER) bifurcation as well.

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