Some rigorous results for the Greenberg-Hastings model

DOI10.1007/BF01259549zbMath0741.92001OpenAlexW2046670719MaRDI QIDQ1181409

Jeffrey E. Steif, Richard T. Durrett

Publication date: 27 June 1992

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01259549

zbMATH Keywords

cell modelcellular automatatopological entropyexcitable mediumstationary distributionsBernoulli shiftsexcited cellrested celltired cell

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Population dynamics (general) (92D25) Entropy and other invariants (28D20) General biology and biomathematics (92B05) Genetics and population dynamics (92D99)

Related Items (10)

Limiting behavior of 3-color excitable media on arbitrary graphs ⋮ Stability of cellular automata trajectories revisited: branching walks and Lyapunov profiles ⋮ Asymptotic Behavior of Excitable Cellular Automata ⋮ Persistence of sums of correlated increments and clustering in cellular automata ⋮ Weak and strong interaction of excitation kinks in scalar parabolic equations ⋮ Cyclic cellular automata and Greenberg-Hastings models on regular trees ⋮ Dynamics and topological entropy of 1D Greenberg–Hastings cellular automata ⋮ Multicolor particle systems with large threshold and range ⋮ Clustering in the three and four color cyclic particle systems in one dimension ⋮ Two applications of percolation to cellular automata.

Cites Work

• Organizing centers in a cellular excitable medium
• Two moments suffice for Poisson approximations: The Chen-Stein method
• Clustering in the one-dimensional three-color cyclic cellular automaton
• Ergodic theory. Introductory lectures
• Spatial Patterns for Discrete Models of Diffusion in Excitable Media
• Entropy for Group Endomorphisms and Homogeneous Spaces
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