Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-30T15:16:28.335Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on oscillations in a simple model of a chemical reaction

Published online by Cambridge University Press:  17 February 2009

M. Jane Sexton  and
Lawrence K. Forbes
Lawrence K. Forbes
Affiliation:
Department of Mathematics, University of Queensland, Qld, 4072, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate oscillatory behaviour in the famous Belousov-Zhabotinskii chemical reaction, as described by the simple two-variable Oregonator model. It is shown that oscillations are possible only in certain parameter regions. Numerical results are presented, and the presence of fold bifurcations discussed.

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 4 , April 1996 , pp. 451 - 457
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Epstein, I. R., Kustin, K., De Kepper, P. and Orbán, M., “Oscillating chemical reactions”, Scientific American (1983) 97–108.CrossRefGoogle Scholar
[2]Field, R. and Noyes, R., “Oscillations in chemical systems IV. Limit cycle behavior in a model of a real chemical reaction”, The Journal of Chemical Physics 60 (5) (1974).CrossRefGoogle Scholar
[3]Forbes, L. K., “Limit-cycle behaviour in a model chemical reaction: the Sal'nikov thermokinetic oscillator”, Proc. R. Soc. Lond. A 430 (1990) 641–651.Google Scholar
[4]Gray, P. and Scott, S. K., Chemical Oscillations and Instabilities (Clarendon Press, Oxford, 1990).CrossRefGoogle Scholar
[5]Hassard, B., Kazarinoff, N. and Wan, Y-H., Theory and Applications of Hopf Bifurcation, number 41 in London Mathematical Society Lecture Note Series (Cambridge University Press, 1981).Google Scholar
[6]Jordan, D. W. and Smith, P., Nonlinear Ordinary Differential Equations (Clarendon Press, Oxford, 1979).Google Scholar
[7]Tyson, J. J., “Oscillation, bistability and echo waves in model of the Belousov-Zhabotinskii reaction”, Ann. NY Acad. Sci. 316 (1979) 279–95.CrossRefGoogle Scholar