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The Birth And Death Processes Of Hypercycle Spirals

Author

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  • KAZUMASA OIDA

    (ATR Adaptive Communications Research Laboratories, 2-2-2 Hikaridai Seika-cho Soraku-gun, Kyoto 619-0288, Japan)

Abstract

The behavior of hypercycle spirals in a two-dimensional cellular automaton model is analyzed. Each spiral can be approximated by an Archimedean spiral with center, width, and phase change according to Brownian motion. A barrier exists between two spirals if the phase synchronization hypothesis is taken into account, and the occurrence rate of pair decay (simultaneous disappearance of two spirals) can be explained through a random walk simulation with the barrier. Simulation experiments show that adjacent species violation is necessary to create new spirals. A hypercycle system can live for a long time if spirals in the system are somewhat unstable, since new spirals cannot emerge when existing spirals are too stable.

Suggested Citation

  • Kazumasa Oida, 2003. "The Birth And Death Processes Of Hypercycle Spirals," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 515-535.
    • Handle: RePEc:wsi:acsxxx:v:06:y:2003:i:04:n:s0219525903001018
    DOI: 10.1142/S0219525903001018
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