Figure 3

Illustration of the bunch variables in the Watanabe–Strogatz formalism. Just like the Kuramoto order parameter \(Z_{\sigma}\), the bunch amplitude and bunch phase in \(z_{\sigma}=\rho_{\sigma}e^{i \varPhi _{\sigma}}\) characterize the level of synchrony. The quantities \(Z_{\sigma}\) and \(z_{\sigma}\) do however only coincide if the population is fully synchronized or for uniformly distributed constants of motion in the limit \({N\rightarrow\infty}\) (see text). The phase distribution variable \(\varPsi_{\sigma}\) is related to the shift and distribution of individual oscillators with respect to \(\varPhi_{\sigma}\)