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We consider a mean-field model of coupled phase oscillators with quenched disorder in the natural frequencies and coupling strengths. A fraction $p$ of oscillators are positively coupled, attracting all others, while the remaining fraction…

Statistical Mechanics · Physics 2016-11-03 Hyunsuk Hong , Kevin P. O'Keeffe , Steven H. Strogatz

Collective oscillations and patterns of synchrony have long fascinated researchers in the applied sciences, particularly due to their far-reaching importance in chemistry, physics, and biology. The Kuramoto model has emerged as a…

Dynamical Systems · Mathematics 2025-10-24 Jason Bramburger , Matt Holzer

We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent…

Chaotic Dynamics · Physics 2015-06-19 M. Komarov , A. Pikovsky

We study phase locking in the Kuramoto model of coupled oscillators in the special case where the number of oscillators, $N$, is large but finite, and the oscillators' natural frequencies are evenly spaced on a given interval. In this case,…

Dynamical Systems · Mathematics 2016-06-29 Bertrand Ottino-Loffler , Steven Strogatz

The number $\mathcal{N}$ of stable fixed points of locally coupled Kuramoto models depends on the topology of the network on which the model is defined. It has been shown that cycles in meshed networks play a crucial role in determining…

Adaptation and Self-Organizing Systems · Physics 2017-03-27 Robin Delabays , Tommaso Coletta , Philippe Jacquod

Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent…

Adaptation and Self-Organizing Systems · Physics 2016-01-19 Francisco A. Rodrigues , Thomas K. DM. Peron , Peng Ji , Jürgen Kurths

In this paper we address two questions about the synchronization of coupled oscillators in the Kuramoto model with all-to-all coupling. In the first part we use some classical results in convex geometry to prove bounds on the size of the…

Dynamical Systems · Mathematics 2021-08-11 Jared C. Bronski , Thomas E. Carty , Lee DeVille

The classical Kuramoto model consists of finitely many pairwise coupled oscillators on the circle. In many applications a simple pairwise coupling is not sufficient to describe real-world phenomena as higher-order (or group) interactions…

Dynamical Systems · Mathematics 2023-05-25 Christian Bick , Tobias Böhle , Christian Kuehn

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

Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean…

Chaotic Dynamics · Physics 2017-06-19 Xiyun Zhang , Arkady Pikovsky , Zonghua Liu

Networks of coupled dynamical units give rise to collective dynamics such as the synchronization of oscillators or neurons in the brain. The ability of the network to adapt coupling strengths between units in accordance with their activity…

Adaptation and Self-Organizing Systems · Physics 2023-05-17 Benjamin Jüttner , Erik Andreas Martens

A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of limit-cycle oscillators of distributed frequencies that are globally coupled…

Adaptation and Self-Organizing Systems · Physics 2020-09-08 Mrinal Sarkar , Shamik Gupta

We study systems of Kuramoto oscillators, driven by one pacemaker, on $d$-dimensional regular topologies like linear chains, rings, hypercubic lattices and Cayley-trees. For the special cases of next-neighbor and infinite-range…

Statistical Mechanics · Physics 2007-05-23 Filippo Radicchi , Hildegard Meyer-Ortmanns

The present paper introduces a linear reformulation of the Kuramoto model describing a self-synchronizing phase transition in a system of globally coupled oscillators that in general have different characteristic frequencies. The…

Pattern Formation and Solitons · Physics 2008-03-18 David C. Roberts

The synchronization transition of correlated ensembles of coupled Kuramoto oscillators on sparse random networks is investigated. Extensive numerical simulations show that correlations between the native frequencies of adjacent oscillators…

Statistical Mechanics · Physics 2010-06-16 Markus Brede

We study the asymptotic clustering (phase-locking) dynamics for the Kuramoto model. For the analysis of emergent asymptotic patterns in the Kuramoto flow, we introduce the pathwise critical coupling strength which yields a sharp transition…

Dynamical Systems · Mathematics 2020-06-24 Seung-Yeal Ha , Sang Woo Ryoo

Inspired by the Deffuant and Hegselmann-Krause models of opinion dynamics, we extend the Kuramoto model to account for confidence bounds, i.e., vanishing interactions between pairs of oscillators when their phases differ by more than a…

Adaptation and Self-Organizing Systems · Physics 2020-09-29 André Reggio , Robin Delabays , Philippe Jacquod

Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all…

Adaptation and Self-Organizing Systems · Physics 2015-11-18 Can Xu , Yuting Sun , Jian Gao , Tian Qiu , Zhigang Zheng , Shuguang Guan

We study the Kuramoto model on complex networks, in which natural frequencies of phase oscillators and the vertex degrees are correlated. Using the annealed network approximation and numerical simulations we explore a special case in which…

Disordered Systems and Neural Networks · Physics 2013-03-14 B. C. Coutinho , A. V. Goltsev , S. N. Dorogovtsev , J. F. F. Mendes

We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the…

Adaptation and Self-Organizing Systems · Physics 2015-01-28 Celso Freitas , Elbert Macau , Arkady Pikovsky