Simulating global properties of electroencephalograms with minimal random neural networks

Peter beim Graben, Juergen Kurths

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


The human electroencephalogram (EEG) is globally characterized by a 1/f power spectrum superimposed with certain peaks, whereby the "alpha peak" in a frequency range of 8-14 Hz is the most prominent one for relaxed states of wakefulness. We present simulations of a minimal dynamical network model of leaky integrator neurons attached to the nodes of an evolving directed and weighted random graph (an Erdos-Renyi graph). We derive a model of the dendritic field potential (DFP) for the neurons leading to a simulated EEG that describes the global activity of the network. Depending on the network size, we find an oscillatory transition of the simulated EEG when the network reaches a critical connectivity. This transition, indicated by a suitably defined order parameter, is reflected by a sudden change of the network's topology when super-cycles are formed from merging isolated loops. After the oscillatory transition, the power spectra of simulated EEG time series exhibit a 1/f continuum superimposed with certain peaks. (c) 2007 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)999-1007
Number of pages9
Issue number4-6
Early online date16 Mar 2007
Publication statusPublished - Jan 2008


  • EEG
  • field potentials
  • leaky integrator units
  • random graphs
  • phase transitions
  • order parameter


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