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Cellular Automata Models Of Ring Dynamics

Author

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  • JANKO GRAVNER

    (Mathematics Department, University of California, Davis, CA 95616, USA)

Abstract

This paper describes three models arising from the theory of excitable media, whose primary visual feature are expanding rings of excitation. Rigorous mathematical results and experimental/computational issues are both addressed. We start with the much-studiedGreenberg–Hastings model (GHM)in which the rings are very short-lived, but they do have a transient percolation property. By contrast, in the model we callannihilating nested rings (ANR), excitation centers only gradually lose strength, i.e., each time they become inactive (and then stay so forever) with a fixed probability; we show how the long-term global connectivity properties of the set of excited sites undergo a phase transition. Second part of the paper is devoted todigital boiling (DB)in which new rings spontaneously appear at rested sites with a positive probability. We focus on such (related) issues as convergence to equilibrium, equilibrium excitation level and success of the basic coupling.

Suggested Citation

  • Janko Gravner, 1996. "Cellular Automata Models Of Ring Dynamics," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(06), pages 863-871.
    • Handle: RePEc:wsi:ijmpcx:v:07:y:1996:i:06:n:s0129183196000715
    DOI: 10.1142/S0129183196000715
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