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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.

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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 

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

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