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Related papers: On synchronization in Kuramoto models on spheres

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Emergence of generalized synchronization patterns in a ring of identical and locally coupled Kuramoto-type rotators are investigated by different methods. These approaches offer a useful visual picture for understanding the complexity of…

Pattern Formation and Solitons · Physics 2019-07-24 Károly Dénes , Bulcsú Sándor , Zoltán Néda

The understanding of synchronization ranging from natural to social systems has driven the interests of scientists from different disciplines. Here, we have investigated the synchronization dynamics of the Kuramoto dynamics departing from…

Disordered Systems and Neural Networks · Physics 2009-09-29 Jie Ren , Huijie Yang

The Kuramoto model with high-order coupling has recently attracted some attention in the field of coupled oscillators in order, for instance, to describe clustering phenomena in sets of coupled agents. Instead of considering interactions…

Adaptation and Self-Organizing Systems · Physics 2019-11-27 Robin Delabays

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 present a detailed analysis of the stability of synchronized solutions to the Kuramoto system of oscillators. We derive an analytical expression counting the dimension of the unstable manifold associated to a given stationary solution.…

Dynamical Systems · Mathematics 2015-06-03 Jared C. Bronski , Lee DeVille , Moon Jip Park

We propose a framework for achieving perfect synchronization in complex networks of Sakaguchi-Kuramoto oscillators in presence of higher order interactions (simplicial complexes) at a targeted point in the parameter space. It is achieved by…

Physics and Society · Physics 2023-03-17 Sangita Dutta , Prosenjit Kundu , Pitambar Khanra , Chittaranjan Hens , Pinaki Pal

We study Kuramoto phase oscillators with temporal fluctuations in the frequencies. The infinite-dimensional system can be reduced in a Gaussian approximation to two first-order differential equations. This yields a solution for the…

Statistical Mechanics · Physics 2013-11-12 Bernard Sonnenschein , Lutz Schimansky-Geier

We examine the impact of time delay on two coupled massive oscillators within the second-order Kuramoto model, which is relevant to the operations of real-world networks that rely on signal transmission speed constraints. Our analytical and…

Chaotic Dynamics · Physics 2024-08-30 Esmaeil Mahdavi , Mina Zarei , Farhad Shahbazi

A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a…

Adaptation and Self-Organizing Systems · Physics 2015-12-02 Rafael S. Pinto , Alberto Saa

Synchronization on the sphere is important to certain control applications in swarm robotics. Of recent interest is the Lohe model, which generalizes the Kuramoto model from the circle to the sphere. The Lohe model is mainly studied in…

Optimization and Control · Mathematics 2020-04-02 Johan Markdahl , Daniele Proverbio , Jorge Goncalves

We study the synchronization of oscillators with inertias and phase shifts, namely the second-order Kuramoto-Sakaguchi model. Using the self-consistent method, we find that the effect of inertia is the introduction of effective phase…

Adaptation and Self-Organizing Systems · Physics 2020-12-29 Jian Gao , Konstantinos Efstathiou

The mean-field Kuramoto model for synchronization of phase oscillators with an asymmetric bimodal frequency distribution is analyzed. Breaking the reflection symmetry facilitates oscillator synchronization to rotating wave phases. Numerical…

patt-sol · Physics 2009-10-30 J. A. Acebron , L. L. Bonilla , S. De Leo , R. Spigler

In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a…

Statistical Mechanics · Physics 2024-04-03 Alejandro P. Riascos

For the Kuramoto model and its variations, it is difficult to analyze the exponential synchronization under the general digraphs due to the lack of symmetry. %due to the asymmetry of the adjacency matrices. In this paper, for the…

Optimization and Control · Mathematics 2018-08-23 Jinxing Zhang , Jiandong Zhu

We explore both analytically and numerically an ensemble of coupled phase-oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time-delay (due to finite signal-propagation…

Adaptation and Self-Organizing Systems · Physics 2015-06-16 Liam Timms , Lars Q. English

The second-order Kuramoto equation describes synchronization of coupled oscillators with inertia, which occur in power grids for example. Contrary to the first-order Kuramoto equation it's synchronization transition behavior is much less…

Statistical Mechanics · Physics 2023-01-16 Géza Ódor , Shengfeng Deng

Synchronization is a ubiquitous phenomenon in complex systems. The Kuramoto model serves as a paradigmatic framework for understanding how coupled oscillators achieve collective rhythm. Conventional approaches focus on pairwise…

Adaptation and Self-Organizing Systems · Physics 2026-03-16 Zheng Wang , Jinjie Zhu , Xianbin Liu

The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost…

Adaptation and Self-Organizing Systems · Physics 2025-05-16 Seungjae Lee , Lucas Braun , Frieder Bönisch , Malte Schröder , Moritz Thümler , Marc Timme

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

In this paper, we study the convergence to the stable equilibrium for Kuramoto oscillators. Specifically, we derive estimates on the rate of convergence to the global equilibrium for solutions of the Kuramoto-Sakaguchi equation in a large…

Analysis of PDEs · Mathematics 2024-06-21 Javier Morales , David Poyato