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Excitable chemical reaction systems

II. Several pulses on the ring fiber

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Summary

The parameters of the Field, Noyes and Körös model for the Belousov-Zhabotinskii reaction were chosen in such a way that the given system is excitable. It is shown by simulation that several pulses on the ring fiber, contrary to experience with known excitable media, may arrange themselves in a nonsymmetrical manner while the equilibrium distances are stable. The condition for such behavior is the non-monotonic dependence of the propagation velocity, v, on the time, T, elapsed since the previous excitation at that point.

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References

  • Arschavskii, Yu. I., Berkinblit, M. B., Dunnin-Barkovskii, V. L.: Propagation of Pulses in a Ring of Excitable Tissues. Biofizika 10, 1048–1054 (1965).

    Google Scholar 

  • Field, R. J., Körös, E., Noyes, R. M.: Oscillation in Chemical Systems II. J. Am. Chem. Soc. 94, 8649–8664 (1972).

    Google Scholar 

  • Fitzhugh, R.: Mathematical Models of Excitation and Propagation in Nerve, p. 1–85, in: Biological Engineering (Schwan, H. P., ed.). New York: McGraw-Hill 1969.

    Google Scholar 

  • Gerisch, O.: Naturwissenschaften 58, 430–437 (1971).

    Google Scholar 

  • Karfunkel, H. R., Seelig, F. F.: Excitable Chemical Reaction Systems I. Definition of Excitability and Simulation of Model Systems. J. Math. Biol. 2, 123–132 (1975).

    Google Scholar 

  • Krinsky, V. I.: Excitation and Wave Propagation During Heart Fibrillation, in: Biological and Biochemical Oscillators (Chance, B., Pye, E. K., Ghosh, A. K., Hess, B., eds.). New York-London: Academic Press 1973.

    Google Scholar 

  • Tyson, J. J.: The Belousov-Zhabotinskii Reaction. (Lecture Notes in Biomathematics, Vol. 10.) 1976.

  • Wiener, N., Rosenblyut, A.: Kibernet. sborn. 3, 7 (1961).

    Google Scholar 

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Karfunkel, H.R., Kahlert, C. Excitable chemical reaction systems. J. Math. Biology 4, 183–185 (1977). https://doi.org/10.1007/BF00275983

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  • DOI: https://doi.org/10.1007/BF00275983

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