The Kuramoto model describes a large population of coupled limit-cycle oscillators whose
natural frequencies are drawn from some prescribed distribution. If the coupling strength …

This article explores the Kuramoto model describing the synchronization of a population of
coupled oscillators. Two versions of this model are considered: a discrete version suitable …

We present the finite-size Kuramoto model analytically continued from real to complex
variables and analyze its collective dynamics. For strong coupling, synchrony appears …

The study of synchronization is a classic topic in nonlinear science. Sometimes the concern
is with mutual synchronization, as in Huygens's 1665 discovery of the sympathy of pendulum …

We solve a long-standing stability problem for the Kuramoto model of coupled oscillators.
This system has attracted mathematical attention, in part because of its applications in fields …

We analyze a large system of globally coupled phase oscillators whose natural frequencies
are bimodally distributed. The dynamics of this system has been the subject of long-standing …

We present a detailed analysis of the stability of phase-locked solutions to the Kuramoto
system of oscillators. We derive an analytical expression counting the dimension of the …

We discuss the asymptotic complete phase–frequency synchronization for the Kuramoto
phase model with a finite size N. We present sufficient conditions for initial configurations …

We analyze a minimal model of a population of identical oscillators with a nonlinear
coupling—a generalization of the popular Kuramoto model. In addition to well-known for the …

The phenomenon of spontaneous synchronization, particularly within the framework of the
Kuramoto model, has been a subject of intense research over the years. The model …