Bootstrap Percolation in Living Neural Networks

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29 Scopus citations


Recent experimental studies of living neural networks reveal that their global activation induced by electrical stimulation can be explained using the concept of bootstrap percolation on a directed random network. The experiment consists in activating externally an initial random fraction of the neurons and observe the process of firing until its equilibrium. The final portion of neurons that are active depends in a non linear way on the initial fraction. The main result of this paper is a theorem which enables us to find the final proportion of the fired neurons, in the asymptotic case, in the case of random directed graphs with given node degrees as the model for interacting network. This gives a rigorous mathematical proof of a phenomena observed by physicists in neural networks.

Original languageEnglish (US)
Pages (from-to)459-475
Number of pages17
JournalJournal of Statistical Physics
Issue number3
StatePublished - 2010
Externally publishedYes


  • Bootstrap percolation
  • Neural networks
  • Phase transition
  • Random graphs

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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