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The Kuramoto model is the paradigmatic model to study synchronization in coupled oscillator systems. In its classical formulation, the oscillators move on the unit circle, each characterized by a scalar phase and a natural frequency, by…

Statistical Mechanics · Physics 2026-03-10 Anna Gallo , Renaud Lambiotte , Timoteo Carletti

Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior. It is interesting to ask how the structural organization of network interactions influences this process. Several…

Adaptation and Self-Organizing Systems · Physics 2017-09-13 Lia Papadopoulos , Jason Kim , Jurgen Kurths , Danielle S. Bassett

Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously…

Adaptation and Self-Organizing Systems · Physics 2018-08-23 Stefano Gherardini , Shamik Gupta , Stefano Ruffo

The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a {\it frustrated} version that…

Adaptation and Self-Organizing Systems · Physics 2022-10-05 Guilhermo L. Buzanello , Ana Elisa D. Barioni , Marcus A. M. de Aguiar

Nature is pervaded with oscillatory dynamics. In networks of coupled oscillators patterns can arise when the system synchronizes to an external input. Hence, these networks provide processing and memory of input. We present a universal…

Machine Learning · Computer Science 2025-06-23 Thomas Geert de Jong , Hirofumi Notsu , Kohei Nakajima

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

Synchronization is a fundamental phenomenon in complex systems, observed across a wide range of natural and engineered contexts. The Kuramoto model provides a foundational framework for understanding synchronization among coupled…

Adaptation and Self-Organizing Systems · Physics 2026-02-03 Riccardo Muolo , Hiroya Nakao , Marco Coraggio

By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…

Networking and Internet Architecture · Computer Science 2024-11-20 Agostino Funel

The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…

Disordered Systems and Neural Networks · Physics 2013-05-30 Luce Prignano , Albert Diaz Guilera

The Kuramoto model is a classical nonlinear ODE system designed to study synchronization phenomena. Each equation represents the phase of an oscillator and the coupling between them is determined by a graph. There is an increasing interest…

Probability · Mathematics 2025-10-02 Cecilia De Vita , Pablo Groisman , Ruojun Huang

We study the synchronisation properties of the Kuramoto model of coupled phase oscillators on a general network. Here we distinguish the ability of such a system to self-synchronise from the stability of this behaviour. While…

Pattern Formation and Solitons · Physics 2015-05-14 Alexander C. Kalloniatis

In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is…

Adaptation and Self-Organizing Systems · Physics 2024-02-21 Albert Díaz-Guilera , Dimitri Marinelli , Conrad J. Pérez-Vicente

The dynamics of large systems of coupled oscillators is a subject of increasing importance with prominent applications in several areas such as physics and biology. The Kuramoto model, where a set of oscillators move around a circle…

Adaptation and Self-Organizing Systems · Physics 2021-11-24 Ana Elisa D. Barioni , Marcus A. M. de Aguiar

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

An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…

Dynamical Systems · Mathematics 2014-05-13 Vishaal Krishnan , Arun D. Mahindrakar , Somashekhar S. Hiremath

Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models,…

Adaptation and Self-Organizing Systems · Physics 2023-05-30 Marco Nurisso , Alexis Arnaudon , Maxime Lucas , Robert L. Peach , Paul Expert , Francesco Vaccarino , Giovanni Petri

In this paper, by extending the concept of Kuramoto oscillator to the left-invariant flow on general Lie group, we investigate the generalized phase synchronization on networks. The analyses and simulations of some typical dynamical systems…

Statistical Mechanics · Physics 2015-06-25 Zhi-Ming Gu , Ming Zhao , Tao Zhou , Chen-Ping Zhu , Bing-Hong Wang

Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to…

Optimization and Control · Mathematics 2011-06-28 Florian Dorfler , Francesco Bullo

The Kuramoto model of coupled phase oscillators is often used to describe synchronization phenomena in nature. Some applications, e.g., quantum synchronization and rigid-body attitude synchronization, involve high-dimensional Kuramoto…

Optimization and Control · Mathematics 2022-03-15 Johan Markdahl , Johan Thunberg , Jorge Goncalves

We establish a unified synchronization framework for the all-to-all hybrid Kuramoto model that couples first- and second-order oscillators within a single dynamical system. Although the Kuramoto model has become one of the most widely used…

Dynamical Systems · Mathematics 2025-12-09 Ting-Yang Hsiao , Yun-Feng Lo , Chengbin Zhu