Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Chaos in the Zhabotinskii reaction

Abstract

THE Belousov–Zhabotinskii reaction is a chemical Bonhoeffer–van der Pol circuit, that is, a relaxation oscillator that can be run as both an astable and a monostable ‘flip-flop’1–3. Apparently the reaction also belongs to the slightly more complicated class of‘universal circuits’4 as introduced by Khaikin5–6. Oscillators of this type not only show ‘smooth’ and ‘relaxation type’ oscillations5–6, but also ‘chaotic’ oscillations4. As evidenced by the simplest equation of this type7, both ‘spiral type’ and ‘screw type’ chaos20 are possible in such systems. We present here preliminary evidence for the occurrence of screw-type chaos in the Zhabotinskii reaction.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Similar content being viewed by others

References

  1. Rössler, O. E. & Hoffmann, D. in Analysis and Simulation of Biochemical Systems (eds Hemker, M. C. & Hess, B.) 91–101 (North-Holland, Amsterdam, 1972).

    Google Scholar 

  2. Winfree, A. T. Science 175, 634–636 (1972).

    Article  ADS  CAS  Google Scholar 

  3. Rössler, O. E. in Physics and Mathematics of the Nervous System (eds Conrad M., Güttinger, W. & Dal Cin, M.) (Springer-Verlag, New York, 1974), Lecture Notes in Biomathematics 4, 546–552 (1974).

    Book  Google Scholar 

  4. Rössler, O. E. Z. Naturforsch. 31a, 259–264 (1976).

    Article  ADS  Google Scholar 

  5. Khaikin, S. E. Zh. prikl. fiz. 7 (1930).

  6. Adronov, A. A., Khaikin, S. E. & Vitt, A. A. Theory of Oscillators 725–729 (Pergamon, New York, 1966).

    Google Scholar 

  7. Rössler, O. E. Phys. Lett. 57a, 397–398 (1976); Z. Naturforsch. 31a, 1664–1670 (1976) Bull. Math. Biol. 39, 275–289 (1977).

    Article  Google Scholar 

  8. Noyes, R. M., Field, R. J. & Köros, E. J. Am. chem. Soc. 94, 1394–1395 (1972).

    Article  CAS  Google Scholar 

  9. Field, R. J., Köros, E. & Noyes, R. M. J. Am. chem. Soc. 94, 8649–8664 (1972).

    Article  CAS  Google Scholar 

  10. Juro, J. J. & Noyes, R. M. J. Am. chem. Soc. 97, 5422–5430 (1975).

    Article  Google Scholar 

  11. Noyes, R. M. & Juro, J. J. J. Am. chem. Soc. 97, 5431–5433 (1975).

    Article  CAS  Google Scholar 

  12. Rössler, O. E. Z. Naturforsch. 32a, 607–613 (1977).

    Article  ADS  Google Scholar 

  13. Li, T. Y. & Yorke, J. A. Am. Math. Monthly 82, 985–992 (1975).

    Article  Google Scholar 

  14. Junkers, G. thesis, Univ. Aachen (1969).

  15. Sørensen, P. B. in Physical Chemistry of Oscillatory Phenomena, (ed. Gray, P.) Faraday Symposium No. 9, p. 150, (Faraday Society, London, 1974).

    Google Scholar 

  16. Winfree, A. T. Science 181, 937–939 (1973).

    Article  ADS  CAS  Google Scholar 

  17. Rössler, O. E. in Synergetics–A Workshop (ed. Haken, H.) 174–183 (Springer New York and Heidelberg, 1977).

    Book  Google Scholar 

  18. Kuramoto, Y. & Yamada, T. Prog. theor. Phys. 56, 679–683 (1976).

    Article  ADS  CAS  Google Scholar 

  19. Rössler, O. E. Z. Naturforsch. 31a, 1168–1172 (1976).

    Article  ADS  Google Scholar 

  20. Rössler, O. E. in Synergetics–A Workshop (ed. Haken, H.) 184–199 (Springer, New York and Heidelberg, 1977).

    Book  Google Scholar 

  21. Olsen, L. F. thesis, Univ. Odense (1977).

  22. Olsen, L. F. & Degn, H. Nature 267, 177–178 (1977).

    Article  ADS  CAS  Google Scholar 

  23. Graziani, K. R., Hudson, J. L. & Schmitz, R. A. Chem. Engng J. 12, 9–15 (1976).

    Article  CAS  Google Scholar 

  24. Schmitz, R. A., Graziani, K. R. & Hudson, J. L. J. chem. Phys. 67, 3040–3044 (1977).

    Article  ADS  CAS  Google Scholar 

  25. Rössler, O. E. Chemiedozententagung, Marburg, 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

ROSSLER, O., WEGMANN, K. Chaos in the Zhabotinskii reaction. Nature 271, 89–90 (1978). https://doi.org/10.1038/271089a0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/271089a0

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing