  Due to time delays in signal transmission and processing, phase lags are
inevitable in realistic complex oscillator networks. Conventional wisdom is
that phase lags are detrimental to network synchronization. Here we show that
judiciously chosen phase lag modulations can result in significantly enhanced
network synchronization. We justify our strategy of phase modulation,
demonstrate its power in facilitating and enhancing network synchronization
with synthetic and empirical network models, and provide an analytic
understanding of the underlying mechanism. Our work provides a new approach to
synchronization optimization in complex networks, with insights into control of
complex nonlinear networks.
