Figure 2.

Simulation of the system (2) for N = 20 oscillators with the parameters A = B = 1, $\alpha =\beta =0.3\pi$ and ${\omega }_0=1.4$. In panel a) the natural frequencies of the oscillators are identical and set to 0; in panel b) ω _i are randomly chosen from the Gaussian distribution with the zero mean and the standard deviation 0.1. Time-dependence of the phase of the leader $\phi (t)$ (dashed green line), the phases ${\varphi }_k(t)$ of the leaves (solid blue lines) and their order parameter (dotted red line). Note that the difference between the blue branches is exactly 2π. (Insets) Snapshots of the oscillators. The leaves are represented as blue circles and the leader as a green diamond; the red line is the order parameter of the leaves.