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Related papers: Kuramoto dynamics in Hamiltonian systems

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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

We consider a long-range model of coupled phase-only oscillators subject to a local potential and evolving in presence of thermal noise. The model is a non-trivial generalization of the celebrated Kuramoto model of collective…

Adaptation and Self-Organizing Systems · Physics 2017-01-04 Alessandro Campa , Shamik Gupta

Globally coupled ensembles of phase oscillators serve as useful tools for modeling synchronization and collective behavior in a variety of applications. As interest in the effects of simplicial interactions (i.e., non-additive, higher-order…

Adaptation and Self-Organizing Systems · Physics 2021-01-13 Can Xu , Per Sebastian Skardal

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

We propose a Kuramoto model of coupled oscillators on a time-varying graph, whose dynamics is dictated by a Markov process in the space of graphs. The simplest representative is considering a base graph and then the subgraph determined by…

Probability · Mathematics 2023-07-10 Pablo Groisman , Ruojun Huang , Hernan Vivas

Common models of synchronizable oscillatory systems consist of a collection of coupled oscillators governed by a collection of differential equations. The ubiquitous Kuramoto models rely on an {\em a priori} fixed connectivity pattern…

Populations and Evolution · Quantitative Biology 2020-05-01 Elizabeth A. Tripp , Feng Fu , Scott D. Pauls

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

Now a standard in Nonlinear Sciences, the Kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phenomenology has been sketched in early works, the…

Analysis of PDEs · Mathematics 2018-12-18 Helge Dietert , Bastien Fernandez

We study a system of $N$ interacting particles moving on the unit sphere in $d$-dimensional space. The particles are self-propelled and coupled all to all, and their motion is heavily overdamped. For $d=2$, the system reduces to the classic…

Dynamical Systems · Mathematics 2024-06-19 Max Lipton , Renato Mirollo , Steven H. Strogatz

Recently, there has been considerable interest in the study of spontaneous synchronization, particularly within the framework of the Kuramoto model. The model comprises oscillators with distributed natural frequencies interacting through a…

Statistical Mechanics · Physics 2014-08-29 Shamik Gupta , Alessandro Campa , Stefano Ruffo

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

Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…

Adaptation and Self-Organizing Systems · Physics 2021-11-01 Can Xu , Xiaohuan Tang , Huaping Lü , Karin Alfaro-Bittner , Stefano Boccaletti , Matjaz Perc , Shuguang Guan

Perhaps because of the elegance of the central limit theorem, it is often assumed that distributions in nature will approach singly-peaked, unimodal shapes reminiscent of the Gaussian normal distribution. However, many systems behave…

Adaptation and Self-Organizing Systems · Physics 2020-02-25 Joseph D. Johnson , Daniel M. Abrams

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

Understanding the mechanisms that govern collective synchronization is a paramount task in nonlinear dynamics. While higher-order (many-body) interactions have recently emerged as a powerful framework for capturing collective behaviors,…

Adaptation and Self-Organizing Systems · Physics 2025-12-19 Narumi Fujii , Keisuke Taga , Riccardo Muolo , Bob Rink , Hiroya Nakao

From a viewpoint of stochastic thermodynamics, we derive equations that describe the collective dynamics near the order-disorder transition in the globally coupled XY model and near the synchronization-desynchronization transition in the…

Statistical Mechanics · Physics 2015-05-20 Shin-ichi Sasa

We study the emergent collective behaviors for an ensemble of identical Kuramoto oscillators under the effect of inertia. In the absence of inertial effects, it is well known that the generic initial Kuramoto ensemble relaxes to the…

Dynamical Systems · Mathematics 2017-07-25 Young-Pil Choi , Seung-Yeal Ha , Javier Morales

We study a generalized Kuramoto model in which each oscillator carries two coupled phase variables, representing a minimal swarmalator system. Assuming perfect correlation between the intrinsic frequencies associated with each phase…

Statistical Mechanics · Physics 2025-11-12 Hyunsuk Hong , Jae Sung Lee , Hyunggyu Park

The Kuramoto model is a dynamical system that models the interaction of coupled oscillators. There has been much work to effectively bound the number of equilibria to the Kuramoto model for a given network. By formulating the Kuramoto…

Algebraic Geometry · Mathematics 2024-09-26 Tianran Chen , Evgeniia Korchevskaia , Julia Lindberg

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