ArticleAdvances in applied probability2021
AVALANCHES IN A SHORT-MEMORY EXCITABLE NETWORK.
Article in Advances in applied probability, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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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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