  Neuronal avalanches are a novel mode of activity in neuronal networks,
experimentally found in vitro and in vivo, and exhibit a robust critical
behaviour: These avalanches are characterized by a power law distribution for
the size and duration, features found in other problems in the context of the
physics of complex systems. We present a recent model inspired in
self-organized criticality, which consists of an electrical network with
threshold firing, refractory period and activity-dependent synaptic plasticity.
The model reproduces the critical behaviour of the distribution of avalanche
sizes and durations measured experimentally. Moreover, the power spectra of the
electrical signal reproduce very robustly the power law behaviour found in
human electroencephalogram (EEG) spectra. We implement this model on a variety
of complex networks, i.e. regular, small-world and scale-free and verify the
robustness of the critical behaviour.
