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Wave propagation in excitable media with fast inhibitor diffusion

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Book cover Transport and Structure

Part of the book series: Lecture Notes in Physics ((LNP,volume 532-532))

Abstract

Wave propagation in excitable media with fast inhibitor diffusion is investigated by analytical and numerical methods. The curvature dependence of the velocity of propagating waves is derived and used to explain the appearance of instabilities with respect to transverse perturbations. Numerical simulations show that this instability may lead to the development of spiral turbulence. On the other hand, the computations also demonstrate that in narrow stripes of such excitable media and/or in media with especially chosen nonhomogeneity the spiral turbulence can be suppressed and steadily propagating wave patterns are found instead.

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References

  1. G.H. Markstein, J. Aeronaut. Sci. 3, 18 (1951).

    Google Scholar 

  2. A. Palacios, G.H. Gunarate, M. Gorman, and K.A. Robbins, Chaos 7, 463 (1997).

    Article  MATH  ADS  Google Scholar 

  3. A.P. Aldushin and B.J. Matkowsky, Combustion Sci. and Tech. 133, 293 (1998).

    Article  Google Scholar 

  4. R.C. Brower, D. Kessler, J. Koplik, and H. Levine, Phys. Rev. A 29, 1335 (1984).

    Article  ADS  Google Scholar 

  5. D. Horvath, V. Petrov, S.K. Scott, and K. Showalter, J. Chem. Phys. 98, 6332 (1993).

    Article  ADS  Google Scholar 

  6. K.I. Lee, W.D. McCormick, Q. Quyang, and H.L. Swinney, Science 261, 192 (1993).

    Article  ADS  Google Scholar 

  7. A.T. Winfree, When Time Breaks Down, (Princeton Univ. Press, Princeton 1987).

    Google Scholar 

  8. S.C. Müller and Th. Plesser (eds), Spatio-temporal Organization in Nonequilibrium Systems, (Projekt Verlag, Dortmund 1992).

    Google Scholar 

  9. R. Kapral and K. Showalter (eds) Chemical Waves and Patterns, Kluwer, Dordrecht (1995).

    Google Scholar 

  10. V.S. Zykov, Simulation of Wave Processes in Excitable Media, (Manchester Univ. Press, 1987).

    Google Scholar 

  11. V.S. Zykov, Ann. N.Y. Ac. Sc. 591, 75 (1990).

    Article  ADS  Google Scholar 

  12. A.S. Mikhailov and V.S. Zykov, Physica D 52, 379 (1991).

    Article  ADS  Google Scholar 

  13. O. Steinbock, V.S. Zykov, and S.C. Müller, Phys. Rev. E 48, 3295 (1993).

    Article  ADS  Google Scholar 

  14. V. Pérez-Muñuzuri, M. Gomez-Gesteira, A.P. Muñuzuri, V.A. Davydov, and V. Pérez-Villar, Phys. Rev. E 51, R845 (1995).

    Google Scholar 

  15. Ya.B. Zeldovich, G.I. Barenblatt, V.B. Librovich, and G.M. Makhviladze. Mathematical Theory of Combustion and Explosion, (Consultants Bureau, New York 1985).

    Google Scholar 

  16. A. Hagberg and E. Meron, Phys. Rev. Lett. 72, 2494 (1994).

    Article  ADS  Google Scholar 

  17. A.F.M. Marée and A.V. Panfilov, Phys. Rev. Lett. 78, 1819 (1997).

    Article  ADS  Google Scholar 

  18. V.S. Zykov, A.S. Mikhailov, and S.C. Müller, Phys. Rev. Lett. 81, 2811 (1998).

    Article  ADS  Google Scholar 

  19. A.S. Mikhailov, Foundations of Synergetics I. Distributed Active Systems, (Springer Verlag, Berlin 1990).

    MATH  Google Scholar 

  20. V.S. Zykov and A.A. Petrov, Biophysics 22, 307 (1977).

    Google Scholar 

  21. M. Wellner and A.M. Pertsov, Phys. Rev. E 55, 7656 (1997).

    Article  ADS  Google Scholar 

  22. J.J. Tyson and J.P. Keener, Physica D 32, 327 (1988).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  23. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, (Springer Verlag, Berlin 1984).

    MATH  Google Scholar 

  24. V. Castets, E. Dulos, J. Boissonade, and P. De Kepper, Phys. Rev. Lett. 64, 2953 (1990).

    Article  ADS  Google Scholar 

  25. J. Enderlein and L. Kuhnert, J. Phys. Chem. 100, 19642 (1996).

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Experimentelle Physik, Otto-von-Guericke-Universität, Universitätsplatz 2, D-39106, Magdeburg, Germany

    V. S. Zykov & S. C. Müller

  2. Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195, Berlin, Germany

    A. S. Mikhailov

Authors
  1. V. S. Zykov
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  2. A. S. Mikhailov
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  3. S. C. Müller
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Editor information

Stefan C. Müller Jürgen Parisi Walter Zimmermann

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© 1999 Springer-Verlag

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Zykov, V.S., Mikhailov, A.S., Müller, S.C. (1999). Wave propagation in excitable media with fast inhibitor diffusion. In: Müller, S.C., Parisi, J., Zimmermann, W. (eds) Transport and Structure. Lecture Notes in Physics, vol 532-532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104233

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  • DOI: https://doi.org/10.1007/BFb0104233

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66632-5

  • Online ISBN: 978-3-540-48070-9

  • eBook Packages: Springer Book Archive

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