Figure 2.

The final share of acting nodes r* in the microscopic network simulation for given shares of certainly acting nodes a. (a) With only around half the population being potentially active (i.e, $p=P/N\approx 0.56$) only a low threshold fraction ($\rho =0.2$, purple) causes large shares of the contingent nodes to act. Grey areas indicate values of r* and a that would exceed p. (b) If every node in the network is potentially active ($p=1$), also an intermediate threshold fraction ($\rho =0.5$, green) suffices to cause the entire population to act. In comparison with (a) one also observes that the transition observed for $\rho =0.2$ occurs already for smaller choices of a. For a large threshold fraction ($\rho =0.8$, yellow) no abrupt transition appears such that $r^{⁎}⪅a$ for all considered choices of a and p.