  In systems of coupled oscillators, the effects of complex signaling can be
captured by time delays and phase shifts. Here, we show how time delays and
phase shifts lead to different oscillator dynamics and how synchronization
rates can be regulated by substituting time delays by phase shifts at constant
collective frequency. For spatially extended systems with time delays, we show
that fastest synchronization can occur for intermediate wavelengths, giving
rise to novel synchronization scenarios.
