Fig. 5

\(\sigma ^{\perp }_i \) and \(\sigma _i^z\) vs. dimensionless time \(\tau = \kappa t\) for a scale-free network with \(N = 60\) nodes, see Fig. 2(b). Each curve describes a single node behavior; at (d) - (i) the black bold curves correspond to the main hub with degree \(k_i = 38\) at \(\Delta _i = 0.5\). For (a) - (c) \(J = 0\); for (d) - (f) \(J = J_R = 0.01, J_I = 0\); for (g) - (i) \(J = -J_I = -0.01i, J_R = 0\). The parameters are: \(\Gamma , \gamma _{+,i}, \sigma _{0,i} = 0\) for (a), (d), (g); \(\Gamma = 0.1\); \(\gamma _{+,i} = 0.5\); \(\sigma _{0,i} = 0.99\) for (b), (e), (h): \(\Gamma = 0.1\), \(\gamma _{+,i} = 0.05\); \(\sigma _{0,i} = 0.99\) for (c), (f), (i). Other parameters are \(g/\kappa = 0.5\); \(\sigma ^{\perp }_i (\tau = 0) \simeq 0\); \(\sigma _i^z(\tau = 0) \simeq 1\).