Activity-Dependent Neuronal Model on Complex Networks

Neuronal avalanches are a novel mode of activity in neuronal networks, experimentally found in vitro and in vivo, and exhibit a robust critical behavior: 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 behavior of the distribution of avalanche sizes and durations measured experimentally. Moreover, the power spectra of the electrical signal reproduce very robustly the power law behavior 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 behavior.