The influences of global and local cues on the synchronization rate of interconnected oscillator networks subject to time delays

Synchronization of interconnected oscillator networks under global and local cues is ubiquitous in nature and engineering. However, the influences of global and local cues on the rate of synchronization have not been fully studied. We analyze the roles of global and local cues in the synchronization rate of interconnected oscillator networks subject to time delays. To study the rate of synchronization, we first give a synchronization condition, which can guarantee synchronization of oscillator networks independent of delays. Then we prove that a stronger global cue always leads to a faster rate of synchronization, whereas local cues have no influence on the rate of synchronization when the delays are below a certain value, and they reduce the rate of synchronization when the delays are larger than the value. Finally simulation results are given to illustrate the theoretical results.