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 /spl alpha/, and for arbitrary network sizes N. For small values of /spl alpha/, avalanches comprising only few neurons dominate. At a critical value, /spl alpha//sub 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".