  Networks of living neurons exhibit an avalanche mode of activity,
experimentally found in organotypic cultures. Moreover, experimental studies of
morphology indicate that neurons develop a network of small-world-like
connections, with the possibility of very high connectivity degree. Here we
study a recent model based on self-organized criticality, which consists of an
electrical network with threshold firing and activity-dependent synapse
strengths. We study the model on a scale-free network, the Apollonian network,
which presents many features of neuronal systems. The system exhibits a power
law distributed avalanche activity. The analysis of the power spectra of the
electrical signal reproduces very robustly the power law behaviour with the
exponent 0.8, experimentally measured in electroencephalograms (EEG) spectra.
The exponents are found to be quite stable with respect to initial
configurations and strength of plastic remodelling, indicating that
universality holds for a wide class of brain models.
