Abstract
A dynamical system that can be provoked by a small stimulus to execute a large transient excursion before returning to the original state is called 'excitable'. In the Belousov–Zhabotinsky (BZ) reagent1 such excitation propagates as a travelling pulse of oxidative activity; leaving a point source, it resembles a closed spherical surface. Activity in excitable media can also be self-organized, independent of any recent stimulus. Wavefronts in cross-section then resemble a spiral emanating from a central pivot. In three dimensions the pivot points form a line, a vortex filament, that typically closes in a slowly shrinking 'scroll ring' (Fig. l)2–4. Here we report the results of monitoring this shrinkage quantitatively both in the BZ reagent and in the Oregonator model, leading to the confirmation of mathematical arguments that derive the filament's motion from its local curvature5–8. By additionally observing the predicted rapid unwinding of a coiled vortex filament9 we validate the reaction–diffusion theory of self-organized activity in such excitable media.
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References
Zaikin, A. N. & Zhabotinsky, A. M. Nature 225, 535–537 (1970).
Winfree, A. T. Science 181, 937–939 (1973).
Winfree, A. T. Faraday Symp. chem. Soc. 9, 38–46 (1975).
Welsh, B., Gomatam, J. & Burgess, A. Nature 304, 611–614 (1983).
Panfilov, A. V., Rudenko, A. V. & Krinsky, V. I. Biofizika 31(5), 850–854 (1986).
Keener, J. P. Physica D 31 269–276 (1988).
Ding, D.-F. Physica D (in the press).
Keener, J. P. & Tyson, J. J. Science 239, 1284–1286 (1988).
Winfree, A. T. & Jahnke, W. J. phys. Chem. (in the press).
Jahnke, W., Skaggs, W. E. & Winfree, A. T. J. phys. Chem. (in the press).
Keener, J. P. & Tyson, J. J. Physica D 21, 307–324 (1986).
Nandapurkar, P. J. in Modelling of Wave Processes in Excitable Media (ed. Zykov, V. S.) English translation (Manchester Univ. Press, 1988).
Lugosi, E. & Winfree, A. T. J. comput. Chem. 9(6), 689–701 (1988).
Henze, C., Jahnke, W., Courtemanche, M. & Winfree, A. T. in Science at the John von Neumann Supercomputer Center Vol. 2 (Consortium for Scientific Computing, Princeton, in the press).
Skaggs, W. E., Lugosi, E. & Winfree, A. T. IEEE Trans. Circ. Sys. T-CAS 35(7), 784–787 (1988).
Winfree, A. T. & Strogatz, S. H. Physica D 9, 65–80 (1983).
Winfree, A. T. & Strogatz, S. H. Physica D 9, 333–345 (1983).
Winfree, A. T. & Guilford, W. in Biomathematics and Related Computational problems (ed. Ricciardi, L. M.) 697–716 (Kluwer Academic Publishers, 1988).
Winfree, A. T. in Modelling of Wave Processes in Excitable Media (ed. Zykov, V. S.) English translation (Manchester Univ. Press, 1988).
Winfree, A. T. When Time Breaks Down 181–183 (Princeton Univ. Press, 1987).
Winfree, A. T. in Science at the John von Neumann Supercomputer Center Vol. 1, 125–130 (Consortium for Scientific Computing, Princeton, 1988).
Chen, P.-S. et al. Circ. Res. 62, 1191–1209 (1988).
Shibata, N. et al. Am. J. Physiol. 255, H891–H909 (1988).
Winfree, A. T. J. theor. Biol (in the press).
Winfree, A. T. in Cardiac Electrophysiology from Celt to Bedside (eds Zipes, D. P. & Jalife, J.) (W. B. Saunders Co., in the press).
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Jahnke, W., Henze, C. & Winfree, A. Chemical vortex dynamics in three-dimensional excitable media. Nature 336, 662–665 (1988). https://doi.org/10.1038/336662a0
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DOI: https://doi.org/10.1038/336662a0
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