Figure 4
Shedding of agents from milling states. (a) Critical coupling for localized shedding in a Waxman geometric random graph. Points indicate simulation-determined values while lines indicate mean-field predictions. Plotted are the first three shedding transitions: \(k = 4\) (circles, solid line), \(k = 6\) (squares, dashed line), and \(k = 8\) (diamonds, dotted line). (b) Critical coupling for the single, delocalized shedding transition in a Watts–Strogatz random graph. The Watts–Strogatz graph was composed of 100 agents with an average degree of 10. Inlet panels in (a) and (b) show the predicted unstable mode associated with the upper mean-field bifurcation by solving Eq. (6). Example snapshots for \(\lambda\) just below the respective transitions are shown in (c) and (d) for the two graphs. Locations for the snapshots within the diagrams (a) and (b) are specified with a green x. Other model parameters and plotting conventions are identical to Fig. 1.
