Exponential synchronization rate of Kuramoto oscillators in the presence of a pacemaker

Abstract

The exponential synchronization rate is addressed for Kuramoto oscillators in the presence of a pacemaker. When natural frequencies are identical, we prove that synchronization can be ensured even when the phases are not constrained in an open half-circle, which improves the existing results in the literature. We derive a lower bound on the exponential synchronization rate, which is proven to be an increasing function of pacemaker strength, but may be an increasing or decreasing function of local coupling strength. A similar conclusion is obtained for phase locking when the natural frequencies are non-identical. An approach to trapping phase differences in an arbitrary interval is also given, which ensures synchronization in the sense that synchronization error can be reduced to an arbitrary level.

ICB Affiliated Authors

Authors
Y. Wang and F. J. Doyle III
Date
Type
Peer-Reviewed Article
Journal
IEEE Transactions on Automatic Control
Volume
58
Pages
989–994
Emblems