Fig. 5: Applications to the PowerGrid network.
From: The transition to synchronization of networked systems
Ecl (see text for definition) vs. d, for the Rössler system (see the differential equations in the text). Data in a [in b] refer to ensemble averages over 850 (200) different numerical simulations of the PowerGrid network. As in Fig. 4, the legends of both panels set the color code for the curves corresponding to each of the reported clusters Ci and to the Entire Network (EN). a reports the case of identical Rössler systems, and the error of 6 specific clusters is plotted (see the Supplementary Information for the composition of each of the 6 clusters Ci). The observed sequence of events perfectly matches the predicted one, with an excellent fit with the values d1, . . . , d6. In panel (b) the effects of heterogeneity in the network are reported. Namely, for each node i of the PowerGrid network, the parameter bi in the Rössler equations is randomly sorted from a uniform distribution in the interval [0.1 − ϵ, 0.1 + ϵ]. The curves plotted refer to ϵ = 0.01.
