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Updated: Oct 15, 2025

Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures
Published on: August 1, 2011
AVALANCHES IN A SHORT-MEMORY EXCITABLE NETWORK
Reza Rastegar1, Alexander Roitershtein2
1Occidental Petroleum Corporation and University of Tulsa.
Abstract:
We study propagation of avalanches in a certain excitable network. The model is a particular case of the one introduced in [24], and is mathematically equivalent to an endemic variation of the Reed-Frost epidemic model introduced in [28]. Two types of heuristic approximation are frequently used for models of this type in applications, a branching process for avalanches of a small size at the beginning of the process and a deterministic dynamical system once the avalanche spreads to a significant fraction of a large network. In this paper we prove several results concerning the exact relation between the avalanche model and these limits, including rates of convergence and rigorous bounds for common characteristics of the model.
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