Figure 4
From: Scale-free behavioral cascades and effective leadership in schooling fish
(a) Probability density of the turning angles \(\varphi\) for the Vicsek model with a leader, for different values of the noise intensity \(\eta\), in a system of size \(L=220\). Dashed lines correspond to a non-turning leader. Full lines represent a leader perturbed periodically every 250 time steps. Vertical lines, indicating the departure of the distributions for perturbed and non-perturbed leaders, are estimated at a value \(\varphi _c(\eta ) \simeq 2.4 \pi \eta\). (b) Number of SPPs turning an angle larger than \(\varphi _\mathrm {th}(\eta ) = 2.5 \pi \eta\) in a sequence of 10,000 simulation time steps in the Vicsek model with a periodically perturbed leader, for different values of \(\eta\). (c) Cumulated distribution of sizes \(P_c(s)\) of avalanches induced by a periodically perturbed leader in a system of size \(L=220\) with turning threshold \(\varphi _\mathrm {th}(\eta )\), for different values of the noise intensity. (d) Cumulated distribution of durations \(P_c(t)\) of avalanches induced by a periodically perturbed leader for different values of the noise intensity.
