Journal of Theoretical Probability

, Volume 5, Issue 1, pp 127–152 | Cite as

Multicolor particle systems with large threshold and range

  • R. Durrett


In this paper we consider the Greenberg-Hastings and cyclic color models. These models exhibit (at least) three different types of behavior. Depending on the number of colors and the size of two parameters called the threshold and range, the Greenberg-Hastings model either dies out, or has equilibria that consist of “debris” or “fire fronts”. The phase diagram for the cyclic color models is more complicated. The main result of this paper, Theorem 1, proves that the debris phase exists for both systems.

Key Words

Particle systems cellular automata excitable media cyclic color models Greenberg-Hastings model 


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Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • R. Durrett
    • 1
  1. 1.Cornell UniversityIthaca

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