Fig. 2. Under low degree of input K_ext, the network self-organizes toward a critical state, and shows long-tailed avalanche distributions.

a Distributions of avalanche sizes $\mathcal{P}\left(s\right)$ show power laws over two orders of magnitude for low K_ext. Fitting a truncated power law, b the exponential cutoff s_cut peaks, and c critical exponents α_s approximate 1.5, as expected for critical branching processes. d A maximum-likelihood comparison decides for a power law compared with an exponential fit in the majority of cases. Dashed vertical lines indicate the set of K_ext/N values that have been selected in a. In this and all following figures, the median over runs and (if acquired) trials is shown, and the errorbars show the 5–95% confidence intervals.