Figure 2.

Avalanche statistics generated by the model at ${\mathcal{D}}^{\ast }=0.3$ (a–b, e–g) and at ${\mathcal{D}}^{\ast }=5$ (c-d,h-j), with ${\gamma }_D=15$ and $\theta =1$ and ${\gamma }_i=\gamma =0.05$ for the extrinsic model. (a–b) Comparison between the trajectories of $\mathcal{D}(t)$, $v_i$ and the corresponding discretization in the low-${\mathcal{D}}^{\ast }$ regime for (a) the extrinsic model and (b) the interacting one. (c–d) Same, but in the high-${\mathcal{D}}^{\ast }$ regime. (e–g) If ${\mathcal{D}}^{\ast }$ is low, avalanches are power-law distributed with almost identical exponents in the extrinsic and interacting model, ${\tau }^{\mathrm{ext}}=1.60\pm 0.01$, ${\tau }^{\mathrm{int}}=1.55\pm 0.01$ and ${\tau }_t^{\mathrm{ext}}=1.77\pm 0.01$, ${\tau }_t^{\mathrm{int}}=1.74\pm 0.01$. The crackling-noise relation is verified in both cases. (h–j) Same plots, now in the high-${\mathcal{D}}^{\ast }$ regime. Avalanches are now fitted with an exponential distribution. Notice that larger events, corresponding to periods in which $\mathcal{D}(t)>{\mathcal{D}}^{\ast }$, show up in the distributions’ tails, suggesting that the shift between exponentials and power-laws is smooth. (j) The average avalanche size as a function of the duration scales with an exponent that, as $D^{\ast }$ increases, becomes closer to the trivial one ${\delta }_{\mathrm{fit}}^{\mathrm{ext}}\approx {\delta }_{\mathrm{fit}}^{\mathrm{int}}\approx 1$.