Figure 1A illustrates the dynamics of random networks without and with internode connections. Without any coupling (K = 0), the nodes oscillate independently at their natural frequencies, and the resulting order parameter for the network is r ≈ 0.1. In contrast, the nodes synchronize with sufficiently strong couplings (K = 10), yielding r ≈ 1. Figure 1B shows the dependence of r on K. When K reaches a critical value (K ≈ 0.2 for σω = 0.15), r increases until it saturates at ~1. The effect of the inhomogeneity in the natural frequencies of the nodes is also shown in Figure 1B. Analytically, when the standard deviation σω is scaled by a factor of p, pK is required to obtain an equivalent degree of synchrony (see Appendix). Hence, in the following discussion, we focus on a case where σω = 0.15.
