Skip to main content

Neuronal avalanches recorded in the awake and sleeping monkey do not show a power law but can be reproduced by a self-organized critical model

Self-organized critical (SOC) systems are complex dynamical systems that may express cascades of events, called avalanches [1]. The SOC state was proposed to govern brain function, because of its activity fluctuations over many orders of magnitude, its sensitivity to small input and its long term stability [2, 3]. In addition, the critical state is optimal for information storage and processing [4]. Both hallmark features of SOC systems, a power law distribution f(s) for the avalanche size s and a branching parameter (bp) of unity, were found for neuronal avalanches recorded in vitro [5]. However, recordings in vivo yielded contradictory results [6]. Electrophysiological recordings in vivo only cover a small fraction of the brain, while criticality analysis assumes that the complete system is sampled. We hypothesized that spatial subsampling might influence the observed avalanche statistics. In addition, SOC models can have different connectivity, but always show a power law for f(s) and bp = 1 when fully sampled. This may not be the case under subsampling, however. Here, we wanted to know whether a state change from awake to asleep could be modeled by changing the connectivity of a SOC model without leaving the critical state.

We simulated a SOC model [1] and calculated f(s) and bp obtained from sampling only the activity of a set of 4 × 4 sites, representing the electrode positions in the cortex. We compared these results with results obtained from multielectrode recordings of local field potentials (LFP) in the cortex of behaving monkeys. We calculated f(s) and bp for the LFP activity recorded while the monkey was either awake or asleep and compared these results to results obtained from two subsampled SOC model with different connectivity.

f(s) and bp were very similar for both the experiments and the subsampled SOC model, but in contrast to the fully sampled model, f(s) did not show a power law and bp was smaller than unity. With increasing the distance between the sampling sites, f(s) changed from "apparently supercritical" to "apparently subcritical" distributions in both the model and the LFP data. f(s) and bp calculated from LFP recorded during awake and asleep differed. These changes could be explained by altering the connectivity in the SOC model.

Our results show that subsampling can prevent the observation of the characteristic power law and bp in SOC systems, and misclassifications of critical systems as sub- or supercritical are possible. In addition, a change in f(s) and bp for different states (awake/asleep) does not necessarily imply a change from criticality to sub- or supercriticality, but can also be explained by a change in the effective connectivity of the network without leaving the critical state.


  1. 1.

    Bak P, Tang C, Wiesenfeld K: Self-organized criticality: An explanation of the 1/f noise. Phys Rev Lett. 1987, 59: 381-384. 10.1103/PhysRevLett.59.381.

    PubMed  Article  Google Scholar 

  2. 2.

    Bak P: How nature works: the science of self-organized criticality. 1996, New York: Copernicus Press

    Book  Google Scholar 

  3. 3.

    Jensen HJ: Self-Organized Criticality. 1998, Cambridge University Press, Cambridge, UK

    Book  Google Scholar 

  4. 4.

    Bertschinger N, Natschläger T: Real-time computation at the edge of chaos in recurrent neural networks. Neural Comput. 2004, 16: 1413-1436. 10.1162/089976604323057443.

    PubMed  Article  Google Scholar 

  5. 5.

    Beggs JM, Plenz D: Neuronal avalanches in neocortical circuits. J Neurosci. 2003, 23: 11167-11177.

    CAS  PubMed  Google Scholar 

  6. 6.

    Bedard C, Kroeger H, Destexhe A: Does the 1/f frequency scaling of brain signals reflect self-organized critical states?. Phys Rev Lett. 2006, 97: 118102-10.1103/PhysRevLett.97.118102.

    CAS  PubMed  Article  Google Scholar 

Download references


We want to thank J. Klon-Lipok for help with data acquisition and M. Beian for help with data preproceessing.

Author information



Corresponding author

Correspondence to Viola Priesemann.

Rights and permissions

Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Priesemann, V., Wibral, M. & Munk, M.H. Neuronal avalanches recorded in the awake and sleeping monkey do not show a power law but can be reproduced by a self-organized critical model. BMC Neurosci 10, P161 (2009).

Download citation


  • Critical State
  • Electrophysiological Recording
  • Local Field Potential
  • Hallmark Feature
  • Complex Dynamical System