Criticality of avalanche dynamics in adaptive recurrent networks

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.