Self-organized criticality in a network of interacting neurons

J.D. Cowan, J. Neuman, B. Kiewiet, W. van Drongelen

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    Abstract

    This paper contains an analysis of a simple neural network that exhibits self-organized criticality. Such criticality follows from the combination of a simple neural network with an excitatory feedback loop that generates bistability, in combination with an anti-Hebbian synapse in its input pathway. Using the methods of statistical field theory, we show how one can formulate the stochastic dynamics of such a network as the action of a path integral, which we then investigate using renormalization group methods. The results indicate that the network exhibits hysteresis in switching back and forward between its two stable states, each of which loses its stability at a saddle?node bifurcation. The renormalization group analysis shows that the fluctuations in the neighborhood of such bifurcations have the signature of directed percolation. Thus, the network states undergo the neural analog of a phase transition in the universality class of directed percolation. The network replicates the behavior of the original sand-pile model of Bak, Tang and Wiesenfeld in that the fluctuations about the two states show power-law statistics.
    Original languageUndefined
    Pages (from-to)04030
    Number of pages24
    JournalJournal of statistical mechanics : theory and experiment
    Volume2013
    Issue number4
    DOIs
    Publication statusPublished - 26 Apr 2013

    Keywords

    • phase transitions into absorbing states (theory)
    • renormalization group
    • self-organized criticality (theory)
    • IR-93159
    • neuronal networks (theory)
    • METIS-309653
    • EWI-25291

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