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Part of the book series: NATO ASI Series ((NSSB,volume 244))

Abstract

We use an open two-dimensional spatial reactor, to create sustained crescent-shaped excitation waves (“excyclons”) propagating in the same azimuthal direction in a thin annular layer of BZ medium. They can produce formerly unknown two-dimensional wavetrain patterns. Excyclons spread evenly around the annulus, as is often the case for pulse trains on ring fibres. However, depending on their number, the resulting rotating wavetrain structures may present either the highest symmetry or topological defects that develop in the radial direction. These defects may be locked in relative position or permanently exchanged from one excyclon to another. A dispersion relation is established. Numerical simulations based on a two-variable Tyson-Fife model of the reaction exhibit good qualitative agreement with experimental observations.

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References

  1. Field, R.J. & Burger, M. (eds.) (1985). Oscillating and travelling waves in chemical systems. Wiley.

    Google Scholar 

  2. Markus, M., Miller, S.C. & Nicolis, G. (eds.) (1987). From chemical to biological organization. Springer.

    Google Scholar 

  3. Vidal, C. & Pacault, A. (1982). In Evolution of order and chaos, Haken, H. (ed.). Springer.

    Google Scholar 

  4. Zaikin, A.N. & Zhabotinskii, A.M. (1970). Nature 225, 535.

    Article  ADS  Google Scholar 

  5. Zhabotinskii, A.M. & Zaikin, A.N. (1973). J. Theor. Biol. 40, 45.

    Article  Google Scholar 

  6. Hanusse, P., Vidal, C. & Pagola, A. In ref. [2], p. 99.

    Google Scholar 

  7. Smoes, M.L. (1980). In Dynamics of synergetic systems, Haken, H. (ed.), p. 80. Springer.

    Chapter  Google Scholar 

  8. Pagola, A., Ross, J. & Vidal, C. (1988). J. Phys. Chem. 92, 163.

    Article  Google Scholar 

  9. Agladze, K.I. & Krinski, V.I. (1982). Nature 296, 424.

    Article  ADS  Google Scholar 

  10. Müller, S.C., Plesser, T. & Hess, B. (1987). Physica D24, 71.

    Google Scholar 

  11. Foerster, P., Müller, S. & Hess, B. (1988). Science 241, 685.

    Article  ADS  Google Scholar 

  12. Nagy-Ungvarai, Z. , Müller, S.C., Tyson, J.J. & Hess, B. (1989). J. Phys. Chem. 93, 2760.

    Article  Google Scholar 

  13. De Kepper, P., Epstein, I.R., Kustin, K. & Orban, M. (1982). J. Phys. Chem. 86, 170.

    Article  Google Scholar 

  14. Nagy-Ungvarai, Z. , Müller, S.C. & Hess, B. (1989). Chem. Phys. Lett. 156, 433.

    Article  ADS  Google Scholar 

  15. Sevcikova, A. & Marek, M. (1983). Physica D9, 140.

    Google Scholar 

  16. Avnir, D. & Kagan, M. (1984). Nature 307, 717.

    Article  ADS  Google Scholar 

  17. Nagypal, I., Bazsa, G. & Epstein, I.R. (1986). J.A.C.S. 108, 3635.

    Article  Google Scholar 

  18. Micheau, J.C., Gimenez, M., Borckmans, P. & Dewell, G. (1983). Nature 305, 43.

    Article  ADS  Google Scholar 

  19. Nicolis, G. & Prigogine, I. (1977). Self-organization in nonequilibrium chemical systems. Wiley.

    Google Scholar 

  20. Boissonade, J. (1988). In Dynamic and stochastic processes. Theory and applications. Lima, R., Streit, L. & Videla Mendes, R. (eds). Lisbonne Workshop. Lecture Notes in Physics, Springer.

    Google Scholar 

  21. Ouyang, Q., Boissonade, J., Roux, J.C. & De Kepper, P. (1989). Phys. Lett. 134, 282.

    Article  Google Scholar 

  22. Tarn, W.Y., Vastano, J.A., Swinney, H.L. & Horsthemke, W. (1988). Phys. Rev. Lett. 61, 2163.

    Article  ADS  Google Scholar 

  23. Boissonade, J., Ouyang, Q., Arneodo, A., Elezgaray, J., Roux, J.C. & De Kepper, P. In these Proceedings.

    Google Scholar 

  24. Tarn, W.Y., Horsthemke, W., Noszticzius, Z. & Swinney, H.L. (1988). J. Chem. Phys. 88, 3395.

    Article  ADS  Google Scholar 

  25. Noszticzius, Z., Horsthemke, W., McCormick, W.D., Swinney, H.L. & Tarn, W.Y. (1987). Nature 329, 619.

    Article  ADS  Google Scholar 

  26. Miller, R.N. & Rinzel, J. (1981). Biophys. J. 34, 227.

    Article  ADS  Google Scholar 

  27. Rinzel, J. & Keller, B. (1973). Biophys. J. 13, 1313.

    Article  ADS  Google Scholar 

  28. Karfunkel, H.R. & Kahlert, C. (1977). J. Math. Biol. 4, 183.

    Article  MATH  Google Scholar 

  29. Tyson, J.J. & Fife, P.C. (1980). J. Chem. Phys. 73 2224.

    Article  ADS  MathSciNet  Google Scholar 

  30. Keener, J.P. & Tyson, J.J. (1986). Physica D21, 307.

    MATH  MathSciNet  Google Scholar 

  31. Dockery, J.D., Keener, J.P. & Tyson, J.J. (1987). Physica D30, 177.

    Google Scholar 

  32. Jahnke, W., Skaggs, W.E. & Winfree, A.T.(1989). J. Chem. Phys. 93, 740.

    Article  Google Scholar 

  33. Arshavskii, Y.I., Berkinblit, M.B. & Dunin-Berkovskii, V.I. (1965). Biophysics 10, 1160.

    Google Scholar 

  34. Ramon, F., Vergara, J. & Moore, J.W. (1973). Biophys. J. 13, 131 (Abstr.).

    Article  Google Scholar 

  35. Donati, F. & Kunov, H. (1979). IEEE Trans. Biomed. Eng. BME 23, 23.

    Google Scholar 

  36. George, S.A. (1977). Biol. Cybernetics 26, 209.

    Article  Google Scholar 

  37. Field, R.J. In ref. [1], Ch. 2, 55.

    Google Scholar 

  38. Tyson, J.J. In ref. [1], Ch. 3, 93.

    Google Scholar 

  39. Nandapurkar, P.J. & Winfree, A.T. (1987). Physica D29, 69;

    MATH  MathSciNet  Google Scholar 

  40. Lugosi, E. & Winfree, A.T. (1988). J. Comp. Chem. 9, 689.

    Article  Google Scholar 

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© 1991 Springer Science+Business Media New York

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Dulos, E., Boissonade, J., De Kepper, P. (1991). Excyclon Dynamics. In: Holden, A.V., Markus, M., Othmer, H.G. (eds) Nonlinear Wave Processes in Excitable Media. NATO ASI Series, vol 244. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3683-7_38

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  • DOI: https://doi.org/10.1007/978-1-4899-3683-7_38

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-3685-1

  • Online ISBN: 978-1-4899-3683-7

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