Asymptotic Frequency Synchronization of Kuramoto Model by Step Force

This paper explains how network topology acts as a control variable for the asymptotic frequency synchronization of the Kuramoto model with finite oscillators. We first investigate the stability of asymptotic frequency synchronization in the Kuramoto model with step force generated by topology switching. We derive a sufficient condition for the asymptotic synchronization. Interestingly, the stability implies that with no constraint on the phase differences or the coupling strength, the asymptotic frequency synchronization can be achieved under certain topology-switching signals. Then, based on the stability of asymptotic frequency synchronization, two triggered topology-switching algorithms are proposed. The step force together with the topology-switching algorithm work as a new frequency synchronization algorithm. Compared with the existing results, the merit of the proposed frequency synchronization algorithms is that they have no constraint on the magnitude of the coupling strength or the phase differences. Simulations are provided to verify the effectiveness of the proposed algorithms.