title: 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.
authors.affiliation: Institute for Collaborative Biotechnologies, University of California, Santa Barbara, California 93106-5080 USA.
authors.forename: Yongqiang
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Institute for Collaborative Biotechnologies, University of California, Santa Barbara, California 93106-5080 USA.
authors.forename: Francis J
authors.initials: FJ
authors.lastname: Doyle
keywords: Exponential synchronization rate; Kuramoto model; oscillator networks; pacemaker