Avalanches of activity in a network of integrate-and-fire neurons with stochastic input

In globally coupled networks of integrate-and-fire neurons with random input, avalanches of spike activity can be observed. We analytically derive an expression for avalanche size distributions valid for arbitrary values of the coupling coefficient α, and for arbitrary network sizes N. For small values of α, avalanches comprising only few neurons dominate. At a critical value, α_crit(N), approximate power-law behavior is observed. Above the critical coupling coefficient, the distribution of avalanche sizes becomes nonmonotonic, thus realizing a kind of “stochastic synchronicity”