The role of pacemakers in the Kuramoto model

Abstract

This work explores the dynamics of synchronization in a coupled system of oscillators, focusing on the role of a mobile pacemaker. Global synchronization, under certain conditions, may emerge when a pacemaker sequentially visits distinct oscillator groups, each with heterogeneous natural frequencies. This approach is applied to the so-called Bluegrass problem, inspired by the coordination of musicians with differing tempos. Numerical simulations reveal dependencies on the pacemaker’s visiting order. Our findings establish that visiting first those communities with higher synchronization levels is optimal. Considering such ordering, convergence to the global synchronized state then follows a power law described by geometric progressions