Figure 4

Avalanche statistics generated by the Wilson Cowan units. The Wilson Cowan units are always in an inhibition dominated phase, i. e. \(\omega _{I} = 7\) and \(\omega _{E} = 6.8\), and \(\alpha = 1\). Their external input h is instead always in a balanced state, in particular \(\omega ^{(h)}_{E} = 50.5\), \(\omega ^{(h)}_{I} = 49.5\). Its other parameters are \(h^{(h)} = 10^{-3}\) and \(\alpha ^{(h)} = 0.1\). In Figures (a–d) however, \(\sigma ^{(h)}\), the amplitude of the noise, is increased to \(2.5 \times 10^{-2}\) so that the up state can be destabilized by the noise. In Figures (e–h) instead the noise is reduced to \(5 \times 10^{-3}\) so that the up state is stable. (a, e) Comparison between the trajectories of h, \(\frac{E_i + I_i}{2}\) and the corresponding trains of events in the high (a) and low (e) \(\sigma ^{(h)}\) regime. (b–d) If \(\sigma ^{(h)}\) is high avalanches are power-law distributed and the crackling-noise relation is verified. (f–g) Same plots, now in the low \(\sigma ^{(h)}\) regime. Avalanches are now fitted with an exponential distribution. (h) The average avalanche size as a function of the duration scales with an exponent that, as \(\sigma ^{(h)}\) decreases, becomes closer to the trivial one \(\delta _\mathrm {fit} \approx 1\).