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We study the synchronization transition of Kuramoto oscillators in scale-free networks that are characterized by tunable local properties. Specifically, we perform a detailed finite size scaling analysis and inspect how the critical…

Statistical Mechanics · Physics 2015-06-25 Jesus Gomez-Gardenes , Yamir Moreno

The Kuramoto model is a classical model used in the study of spontaneous synchronizations in networks of coupled oscillators. In this model, frequency synchronization configurations can be formulated as complex solutions to a system of…

Algebraic Geometry · Mathematics 2019-12-16 Tianran Chen , Evgeniia Korchevskaia

Maintaining the stability of synchronization state is crucial for the functioning of many natural and artificial systems. In this study, we develop methods to optimize the synchronization stability of the Kuramoto model by minimizing the…

Optimization and Control · Mathematics 2017-01-18 Bo Li , K. Y. Michael Wong

In this paper we study synchronization of random clustered networks consisting of Kuramoto oscillators. More specifically, by developing a mean-field analysis, we find that the presence of cycles of order three does not play an important…

Statistical Mechanics · Physics 2012-10-10 Thomas Kauê Dal'Maso Peron , Francisco Aparecido Rodrigues , Jürgen Kurths

This paper studies the synchronization of a finite number of Kuramoto oscillators in a frequency-dependent bidirectional tree network. We assume that the coupling strength of each link in each direction is equal to the product of a common…

Systems and Control · Computer Science 2018-12-11 Matin Jafarian , Xinlei Yi , Mohammad Pirani , Henrik Sandberg , Karl Henrik Johansson

Using a survey of wristwatch synchronization from a randomly selected group of independent volunteers, one can model the system as a Kuramoto-type coupled oscillator network. Based on the phase data, both the order parameter and an…

Adaptation and Self-Organizing Systems · Physics 2010-03-26 Reginald D. Smith

The transient stability of power systems and synchronization of non-uniform Kuramoto oscillators are closely related problems. In this paper, we develop a novel regional stability analysis framework based on the proposed region-parametrized…

Systems and Control · Computer Science 2018-04-06 Lijun Zhu , David J. Hill

We investigate a non-Abelian generalization of the Kuramoto model proposed by Lohe and given by $N$ quantum oscillators ("nodes") connected by a quantum network where the wavefunction at each node is distributed over quantum channels to all…

Analysis of PDEs · Mathematics 2017-08-02 Paolo Antonelli , Pierangelo Marcati

We solve a longstanding stability problem for the Kuramoto model of coupled oscillators. This system has attracted mathematical attention, in part because of its applications in fields ranging from neuroscience to condensed-matter physics,…

Pattern Formation and Solitons · Physics 2009-11-13 Renato Mirollo , Steven H. Strogatz

We propose the idea of using Kuramoto models (including their higher-dimensional generalizations) for machine learning over non-Euclidean data sets. These models are systems of matrix ODE's describing collective motions (swarming dynamics)…

Machine Learning · Computer Science 2024-05-16 Vladimir Jacimovic

A graph $\mathcal{G}$ is referred to as $\mathsf{S}^1$-synchronizing if, roughly speaking, the Kuramoto-like model whose interaction topology is given by $\mathcal{G}$ synchronizes almost globally. The Kuramoto model evolves on the unit…

Optimization and Control · Mathematics 2018-07-27 Johan Markdahl , Johan Thunberg , Jorge Goncalves

The synchronization pattern of a fully connected competing Kuramoto model with a uniform intrinsic frequency distribution $g(\omega)$ was recently considered. This competing Kuramoto model assigns two coupling constants with opposite signs,…

Statistical Mechanics · Physics 2020-09-04 Jinha Park , B. Kahng

Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two…

Adaptation and Self-Organizing Systems · Physics 2023-08-02 Rico Berner , Annie Lu , Igor M. Sokolov

The study of synchronization in populations of coupled biological oscillators is fundamental to many areas of biology to include neuroscience, cardiac dynamics and circadian rhythms. Studying these systems may involve tracking the…

Quantitative Methods · Quantitative Biology 2017-01-18 Kevin M. Hannay , Daniel B. Forger , Victoria Booth

Kuramoto's differential equation describes a synchronization process between several harmonic oscillators. It has been used to model biological phenomena such as the synchronization of heart cells, the circadian rhythm, or brain waves. It…

Dynamical Systems · Mathematics 2026-05-26 Daniel Burns , Gregorio Malajovich , Charles Pugh , Indika Rajapakse , Steve Smale

We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a…

Dynamical Systems · Mathematics 2014-10-29 Andrey Gushchin , Enrique Mallada , Ao Tang

The Kuramoto model is a system of ordinary differential equations for describing synchronization phenomena defined as a coupled phase oscillators. In this paper, a bifurcation structure of the infinite dimensional Kuramoto model is…

Dynamical Systems · Mathematics 2019-02-20 Hayato Chiba

The Kuramoto phase diffusion equation is a nonlinear partial differential equation which describes the spatio-temporal evolution of a phase variable in an oscillatory reaction diffusion system. Synchronization manifests itself in a…

Disordered Systems and Neural Networks · Physics 2009-03-30 Ralf Toenjes , Bernd Blasius

Populations of oscillators are present throughout nature. Very often synchronization is observed in such populations if they are allowed to interact. A paradigmatic model for the study of such phenomena has been the Kuramoto model. However,…

Adaptation and Self-Organizing Systems · Physics 2022-06-08 Keith A. Kroma-Wiley , Peter J. Mucha , Dani S. Bassett

A way to associate unweighted graphs from weighted ones is presented, such that linear stable equilibria of the Kuramoto homogeneous model associated to both graphs coincide, i.e., equilibria of the system $\dot\theta_i = \sum_{j \sim i}…

Combinatorics · Mathematics 2022-10-05 Eduardo A. Canale