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. 2022 Jun 24;12:10770. doi: 10.1038/s41598-022-13686-0

Figure 2.

Figure 2

Avalanche statistics generated by the model at D=0.3 (ab, eg) and at D=5 (c-d,h-j), with γD=15 and θ=1 and γi=γ=0.05 for the extrinsic model. (ab) Comparison between the trajectories of D(t), vi and the corresponding discretization in the low-D regime for (a) the extrinsic model and (b) the interacting one. (cd) Same, but in the high-D regime. (eg) If D is low, avalanches are power-law distributed with almost identical exponents in the extrinsic and interacting model, τext=1.60±0.01, τint=1.55±0.01 and τtext=1.77±0.01, τtint=1.74±0.01. The crackling-noise relation is verified in both cases. (hj) Same plots, now in the high-D regime. Avalanches are now fitted with an exponential distribution. Notice that larger events, corresponding to periods in which D(t)>D, 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 increases, becomes closer to the trivial one δfitextδfitint1.