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
Rössler, O. E. & Hoffmann, D. in Analysis and Simulation of Biochemical Systems (eds Hemker, M. C. & Hess, B.) 91–101 (North-Holland, Amsterdam, 1972).
Winfree, A. T. Science 175, 634–636 (1972).
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).
Rössler, O. E. Z. Naturforsch. 31a, 259–264 (1976).
Khaikin, S. E. Zh. prikl. fiz. 7 (1930).
Adronov, A. A., Khaikin, S. E. & Vitt, A. A. Theory of Oscillators 725–729 (Pergamon, New York, 1966).
Rössler, O. E. Phys. Lett. 57a, 397–398 (1976); Z. Naturforsch. 31a, 1664–1670 (1976) Bull. Math. Biol. 39, 275–289 (1977).
Noyes, R. M., Field, R. J. & Köros, E. J. Am. chem. Soc. 94, 1394–1395 (1972).
Field, R. J., Köros, E. & Noyes, R. M. J. Am. chem. Soc. 94, 8649–8664 (1972).
Juro, J. J. & Noyes, R. M. J. Am. chem. Soc. 97, 5422–5430 (1975).
Noyes, R. M. & Juro, J. J. J. Am. chem. Soc. 97, 5431–5433 (1975).
Rössler, O. E. Z. Naturforsch. 32a, 607–613 (1977).
Li, T. Y. & Yorke, J. A. Am. Math. Monthly 82, 985–992 (1975).
Junkers, G. thesis, Univ. Aachen (1969).
Sørensen, P. B. in Physical Chemistry of Oscillatory Phenomena, (ed. Gray, P.) Faraday Symposium No. 9, p. 150, (Faraday Society, London, 1974).
Winfree, A. T. Science 181, 937–939 (1973).
Rössler, O. E. in Synergetics–A Workshop (ed. Haken, H.) 174–183 (Springer New York and Heidelberg, 1977).
Kuramoto, Y. & Yamada, T. Prog. theor. Phys. 56, 679–683 (1976).
Rössler, O. E. Z. Naturforsch. 31a, 1168–1172 (1976).
Rössler, O. E. in Synergetics–A Workshop (ed. Haken, H.) 184–199 (Springer, New York and Heidelberg, 1977).
Olsen, L. F. thesis, Univ. Odense (1977).
Olsen, L. F. & Degn, H. Nature 267, 177–178 (1977).
Graziani, K. R., Hudson, J. L. & Schmitz, R. A. Chem. Engng J. 12, 9–15 (1976).
Schmitz, R. A., Graziani, K. R. & Hudson, J. L. J. chem. Phys. 67, 3040–3044 (1977).
Rössler, O. E. Chemiedozententagung, Marburg, 1977.
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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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DOI: https://doi.org/10.1038/271089a0
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