Stability of Synchronous Solutions in a Directed Kuramoto-Oscillator Network With a Pacemaker

Abstract

In this brief, we investigate the stability of a directed Kuramoto-oscillator network with a pacemaker for two kinds of synchronous solutions. Sufficient conditions on the coupling strength and initial phases to achieve such synchronous solutions are explicitly provided under the assumption that the augmented digraph has a directed spanning tree rooted at the pacemaker. Moreover, the minimum number of pinned oscillators is determined under the given conditions.