Modelling the brain as a n Apollonian network

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.