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Isotropic Automata for Simulations of Excitable Media: Periodicity, Chaos and Reorganization

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Dissipative Structures in Transport Processes and Combustion

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 48))

Abstract

Cellular automata have been used for the simulation of excitable media as an efficient alternative to partial differential equations. However, the automata proposed so far are anisotropic since the shapes of the propagating waves are related to the shapes of the cells (e.g. squares or hexagons). This problem is solved in the present work by automata based on a random distribution of excitable elements. Using a (minimal) model with only three parameters, the following results are obtained, in good agreement with experiments: periodic patterns in two dimensions (target patterns and spirals) and three dimensions (scroll waves), eikonal relationships (normal velocities as functions of the curvature of the wavefront), spatiotemporal chaos for spatially periodic inhomo-geneities, reorganization after suppression of these inhomogeneities. An extension of the model including two more parameters yields a dispersion relation comparable to that obtained from measurements and from an analysis of the relevant partial differential equations.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Ernährungsphysiologie, Rheinlanddamm 201, D-4600, Dortmund 1, Fed. Rep. of Germany

    M. Markus & B. Hess

Authors
  1. M. Markus
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  2. B. Hess
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Editors and Affiliations

  1. Fakultät für Physik, Universität Bielefeld, Postfach 8640, D-4800, Bielefeld 1, Fed. Rep. of Germany

    Dirk Meinköhn

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© 1990 Springer-Verlag Berlin, Heidelberg

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Markus, M., Hess, B. (1990). Isotropic Automata for Simulations of Excitable Media: Periodicity, Chaos and Reorganization. In: Meinköhn, D. (eds) Dissipative Structures in Transport Processes and Combustion. Springer Series in Synergetics, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84230-6_14

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  • DOI: https://doi.org/10.1007/978-3-642-84230-6_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-84232-0

  • Online ISBN: 978-3-642-84230-6

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