Simulating global properties of electroencephalograms with minimal random neural networks

The human electroencephalogram (EEG) is globally characterized by a 1/f1/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 Erdős–Rényi 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/f1/f continuum superimposed with certain peaks.