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Avalanches in Self-Organized Critical Neural Networks: A Minimal Model for the Neural SOC Universality Class

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  • Matthias Rybarsch
  • Stefan Bornholdt

Abstract

The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. Thus the model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that may include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain.

Suggested Citation

  • Matthias Rybarsch & Stefan Bornholdt, 2014. "Avalanches in Self-Organized Critical Neural Networks: A Minimal Model for the Neural SOC Universality Class," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-8, April.
  • Handle: RePEc:plo:pone00:0093090
    DOI: 10.1371/journal.pone.0093090
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    References listed on IDEAS

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    1. Alberto Mazzoni & Frédéric D Broccard & Elizabeth Garcia-Perez & Paolo Bonifazi & Maria Elisabetta Ruaro & Vincent Torre, 2007. "On the Dynamics of the Spontaneous Activity in Neuronal Networks," PLOS ONE, Public Library of Science, vol. 2(5), pages 1-12, May.
    2. Peng, Jiayi & Beggs, John M., 2013. "Attaining and maintaining criticality in a neuronal network model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1611-1620.
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    Cited by:

    1. Yang, JinHao & Ding, Yiming & Di, Zengru & Wang, DaHui, 2024. "“All-or-none” dynamics and local-range dominated interaction leading to criticality in neural systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 638(C).

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