Nature Publishing Group, publisher of Nature, and other science journals and reference works
Nature
my account e-alerts subscribe register
   
Monday 24 July 2017
Journal Home
Current Issue
AOP
Archive
Download PDF
References
Export citation
Export references
Send to a friend
More articles like this

Letters to Nature
Nature 271, 89 - 90 (05 January 1978); doi:10.1038/271089a0

Chaos in the Zhabotinskii reaction

OTTO E. ROSSLER* & KLAUS WEGMANN

*Institute for Physical and Theoretical Chemistry, University of Tübingen, and Institute for Theoretical Physics, University of Stuttgart
Institute for Chemical Plant Physiology, University of Tübingen, 7400 Tübingen, FRG

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.

------------------

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).
2. Winfree, A. T. Science 175, 634–636 (1972).
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).
4. Rössler, O. E. Z. Naturforsch. 31a, 259–264 (1976).
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).
7. Rössler, O. E. Phys. Lett. 57a, 397–398 (1976); Z. Naturforsch. 31a, 1664–1670 (1976) Bull. Math. Biol. 39, 275–289 (1977).
8. Noyes, R. M., Field, R. J. & Köros, E. J. Am. chem. Soc. 94, 1394–1395 (1972).
9. Field, R. J., Köros, E. & Noyes, R. M. J. Am. chem. Soc. 94, 8649–8664 (1972).
10. Juro, J. J. & Noyes, R. M. J. Am. chem. Soc. 97, 5422–5430 (1975).
11. Noyes, R. M. & Juro, J. J. J. Am. chem. Soc. 97, 5431–5433 (1975).
12. Rössler, O. E. Z. Naturforsch. 32a, 607–613 (1977).
13. Li, T. Y. & Yorke, J. A. Am. Math. Monthly 82, 985–992 (1975).
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).
16. Winfree, A. T. Science 181, 937–939 (1973).
17. Rössler, O. E. in Synergetics–A Workshop (ed. Haken, H.) 174–183 (Springer New York and Heidelberg, 1977).
18. Kuramoto, Y. & Yamada, T. Prog. theor. Phys. 56, 679–683 (1976).
19. Rössler, O. E. Z. Naturforsch. 31a, 1168–1172 (1976).
20. Rössler, O. E. in Synergetics–A Workshop (ed. Haken, H.) 184–199 (Springer, New York and Heidelberg, 1977).
21. Olsen, L. F. thesis, Univ. Odense (1977).
22. Olsen, L. F. & Degn, H. Nature 267, 177–178 (1977).
23. Graziani, K. R., Hudson, J. L. & Schmitz, R. A. Chem. Engng J. 12, 9–15 (1976).
24. Schmitz, R. A., Graziani, K. R. & Hudson, J. L. J. chem. Phys. 67, 3040–3044 (1977).
25. Rössler, O. E. Chemiedozententagung, Marburg, 1977.



© 1978 Nature Publishing Group
Privacy Policy