In many studies of self-organized criticality (SOC), branching processes were used to model the dynamics of the activity of the system during avalanches. This mathematical simplification was also adopted when investigating systems with a complicated connection topology including recurrent and subthreshold interactions. However, none of these studies really analyzed whether this convenient approximation was indeed applicable. In present paper we study the correspondences between avalanches generated by branching processes and by a fully connected neural network. The benefit from the analysis is not only the justification of such correspondence but also a simple learning rule, which allows self-organization of the network towards a critical state as recently observed in slice experiments
Self-organized criticality generates complex behavior in systems of simple elements. It is observed in various biological neural systems and has been analyzed in simplified model systems. Branching processes often considered to be a mean-field approximation to the dynamics of critical systems. Here we study the validity of such an approximation for the case of a neural network.
There is experimental evidence that cortical neurons show avalanche activity with the intensity of firing events being distributed as a power-law. We present a biologically plausible extension of a neural network which exhibits a power-law avalanche distribution for a wide range of connectivity parameters.