The Kuramoto model: A simple paradigm for synchronization phenomena

  title={The Kuramoto model: A simple paradigm for synchronization phenomena},
  author={Juan A. Acebr{\'o}n and Luis L. Bonilla and Conrado J. P{\'e}rez Vicente and Felix Ritort and Renato Spigler},
  journal={Reviews of Modern Physics},
Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods… 
Dynamics of the finite-dimensional Kuramoto model: Global and cluster synchronization
Synchronization phenomena in networks of globally coupled non-identical oscillators have been one of the key problems in nonlinear dynamics over the years. The main model used within this framework
Kuramoto model with coupling through an external medium.
This generalized model of the Kuramoto model is studied where oscillators communicate with each other through an external medium and exhibits interesting new phenomena such as bistability between synchronization and incoherence and a qualitatively new form of synchronization where the external medium exhibits small-amplitude oscillations.
Synchronization in a semiclassical Kuramoto model.
This work derives equations for the Kuramoto model by taking into account the first quantum fluctuations, and analyzes its critical properties, the main result being the derivation of the value for the synchronization onset.
Distribution of Order Parameter for Kuramoto Model
The synchronization in large populations of interacting oscillators has been observed abundantly in nature, emergining in fields such as physical, biological and chemical system. For this reason,
Continuous limit and the moments system for the globally coupled phase oscillators
The Kuramoto model, which describes synchronization phenomena, is a system of ordinary differential equations on $N$-torus defined as coupled harmonic oscillators. The order parameter is often used
Kuramoto model of synchronization: equilibrium and nonequilibrium aspects
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 comprises oscillators with
Synchronization and clustering of phase oscillators with heterogeneous coupling
We generalize Kuramoto's theory for the synchronization transition of globally coupled phase oscillators to populations where each oscillator has a different coupling strength. We show that, beyond
Phase transitions and chaos in long-range models of coupled oscillators
We study the chaotic behavior of the synchronization phase transition in the Kuramoto model. We discuss the relationship with analogous features found in the Hamiltonian mean-field (HMF) model. Our
Synchronization of oscillators in a Kuramoto-type model with generic coupling.
This work presents the explicit solutions of self-consistency equations for the amplitude and frequency of the mean field in a parametric form, valid for noise-free and noise-driven oscillators.


Large Populations of Coupled Chemical Oscillators
  • J. Neu
  • Mathematics, Physics
  • 1980
We study the mechanisms that underlie synchronization processes in large systems of coupled chemical oscillators. By synchronization, we mean the evolution from an initial state where the phases of
Plasticity and learning in a network of coupled phase oscillators.
A generalized Kuramoto model of coupled phase oscillators with a slow varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs of
Solvable Dynamics in a System of Interacting Random Tops
A new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops or magnetic moments with random precession frequencies. The model allows for an
Emerging Coherence in a Population of Chemical Oscillators
Experiments on populations of chemical oscillators and a 25-year-old theory of Kuramoto that predicts that global coupling in a set of smooth limit-cycle oscillators with different frequencies produces a phase transition in which some of the elements synchronize are reported.
Synchronization in a system of globally coupled oscillators with time delay
  • Choi, Kim, Hong
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 2000
Analysis of the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling reveals that the system in general exhibits discontinuous transitions in addition to the usual continuous transition, between the incoherent state and a multitude of coherent states with different synchronization frequencies.
Phase diagram for the Winfree model of coupled nonlinear oscillators.
The first bifurcation analysis of the Winfree mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators is given, for a tractable special case.