Synchronization control in networks with uniform and distributed phase lag

We show that phase lag angles in oscillator networks can be used to control the frequency of synchronized oscillations, either to adjust the common frequency to any preset value, within limits, or else to damp out any highly oscillatory nodes so that the system oscillates almost independently of the phase lag. We investigate in particular the Sakaguchi–Kuramoto model and a generalization with nonisochronous oscillations, for globally connected networks, to show that synchronization occurs under a broad set of conditions for both uniform and distributed phase lag, and find specific formulas for the common frequency of oscillation. The analysis is valid for any finite number of nodes and for arbitrary distributions of phase lag angles and local frequencies, and can be extended to systems with time delayed interactions.