Figure 3B shows the change in the order parameter averaged over the whole network, or the global order parameter, upon the addition of inter-subnetwork connections (Kinter = 10). Prior to the coupling of the two subnetworks, the nodes within each subnetwork are synchronized, as Kintra is sufficiently high (Kintra = 4). However, the synchronizing phases of the two subnetworks are independent, yielding a global order parameter of r ≈ 0.6. When the two subnetworks are coupled at t = 250 s, the global order parameter gradually increases, and the coupled subnetworks synchronize (r > 0.9). Note that although the network does not reach a fully synchronized state (r = 1), the whole network is in a steady state when r saturates (t > 300 s); this is confirmed by observing the distribution of the phase and phase velocity (Figure 3A). The steady state is hence different from the so-called “chimera state,” a state which coherent and incoherent domains coexist in (Laing, 2009) and appears as a transient phase in finite-sized Kuramoto networks (Wolfrum and Omel'chenko, 2011).
