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Bursting Phenomena in the Belousov-Zhabotinsky Reaction

  • John Rinzel
  • William C. Troy
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 12)

Abstract

We [1] have investigated a model for the Belousov-Zhabotinskii reaction in a continuous flow, stirred tank reactor. The model consists of a system of three ordinary differential equations derived from a more complicated five-variable, Oregonator [2] model proposed by JANZ, VANECEK, and FIELD [3]. Over an appropriate range of physical parameters (e.g., lower flow rates) the system exhibits bursts of oscillations. As in some experiments (e.g., MAREK and SVOBODOVA [4]), the observer sees several spikes followed by an interval of quiescence (IQ) which is subsequently followed by a resumption of the spikes, etc. The bursting phenomenon results from a hysteresis loop in which the solution alternates between a stable periodic solution, during the oscillatory phase, and a stable steady state of low oxidation, during the IQ, of a two-variable batch-reactor sub-system. This bistable behavior is due to a subcritical Hopf bifurcation (hard-oscillation) in the two variable system. We have estimated analytically the IQ duration and its dependence on parameter values. For other parameter ranges we find qualitatively different bursting phenomena. In one example the CSTR system is excitable; there is a stable steady state and the response to an adequate perturbation is an excitation burst of several pulses and then a return to the steady state. At considerably higher flow rates, there are repetitive, single-spike bursts with IQ’s of high oxidation; such patterns resemble those calculated by SCHOWALTER, NOYES, and BAR-ELI [5] and observed experimentally by SCHMITZ, GRAZIANI, and HUDSON [6].

Keywords

Periodic Solution Hysteresis Loop Parameter Range High Flow Rate High Oxidation 
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References

  1. 1.
    J. Rinzel, W.C. Troy: J. Chem. Phys. (to appear 1981 )Google Scholar
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    R.J. Field, E. Koros, R.M. Noyes: J. Am. Chem. Soc. 94, 8649 (1972)CrossRefGoogle Scholar
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    D. Janz, D. Vanecek, R.J. Field: J. Chem. Phys. 73, 3132 (1980)CrossRefADSMathSciNetGoogle Scholar
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    M. Marek, E. Svobodova: Biophys. Chem. 3, 263 (1975)CrossRefGoogle Scholar
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    K. Schowalter, R. Noyes, K. Bar-Eli: J. Chem. Phys. 69, 2514 (1978)CrossRefADSGoogle Scholar
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    R.A. Schmitz, K.R. Graziani, J.L. Hudson: J. Chem. Phys. 67, 3040 (1977)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • John Rinzel
    • 1
  • William C. Troy
    • 2
  1. 1.National Institutes of HealthBethesdaUSA
  2. 2.University of PittsburghPittsburghUSA

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