The synchronization rate of oscillator networks subject to delayed and directed interaction

This paper analyzes influences of global and local cues on the synchronization rate of inter-connected oscillator networks subject to time delays. The coupling between oscillators is assumed to be directed, which includes the symmetric bi-directional coupling as a special case. In order to study the rate of synchronization, we first give a synchronization condition, which guarantees synchronization of oscillator networks independent of delays. Then we prove that the rate of synchronization always benefits from a stronger global cue, namely a stronger global cue leads to a faster rate of synchronization. The role of the local cue in the rate of synchronization is proven to be more complex: when the delays are below a certain value, the local cue has no influence on the rate of synchronization, but when the delays are above the value, a stronger local cue lowers the rate of synchronization. Finally, simulation results are given to illustrate the theoretical results.

Wang, Y., Doyle, F.
Proceedings of the 48th Annual Allerton Conference on Communication, Control, and Computing
Pages: 1657 - 1662
City: Allerton
State: IL
Date: September, 2010
ICB Affiliated Authors: Francis J Doyle III, Yongqiang Wang