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We study the global bifurcations of frequency weighted Kuramoto model in low-dimension for network of fully connected oscillators. To study the effect of non-zero-centered frequency distribution, we consider two symmetric Lorentzians as an…

Adaptation and Self-Organizing Systems · Physics 2021-09-07 Sara Ameli , Keivan Aghababaei Samani

We explore the impact of global resetting on Kuramoto-type models of coupled limit-cycle oscillators with distributed frequencies both in absence and presence of noise. The dynamics comprises repeated interruption of the bare dynamics at…

Statistical Mechanics · Physics 2025-07-21 Anish Acharya , Mrinal Sarkar , Shamik Gupta

A family of stochastic processes has quasi-cycle oscillations if the oscillations are sustained by noise. For such a family we define a Kuramoto-type coupling of both phase and amplitude processes. We find that synchronization, as measured…

Dynamical Systems · Mathematics 2015-11-30 Priscilla E. Greenwood , Lawrence M. Ward

The Kuramoto model is a mean-field model for the synchronisation behaviour of oscillators, which exhibits Landau damping. In a recent work, the nonlinear stability of a class of spatially inhomogeneous stationary states was shown under the…

Analysis of PDEs · Mathematics 2020-01-14 Helge Dietert

A generalized Kuramoto model of coupled phase oscillators with slowly varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs of oscillators in such a way that the coupling…

Adaptation and Self-Organizing Systems · Physics 2009-11-07 Philip Seliger , Stephen C. Young , Lev S. Tsimring

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

Phase-locked states with a constant phase shift between the neighboring oscillators are studied in rings of identical Kuramoto oscillators with time-delayed nearest-neighbor coupling. The linear stability of these states is derived and it…

Pattern Formation and Solitons · Physics 2020-04-01 Károly Dénes , Bulcsú Sándor , Zoltán Néda

The Kuramoto--Sakaguchi model is a modification of the well-known Kuramoto model that adds a phase-lag paramater, or "frustration" to a network of phase-coupled oscillators. The Kuramoto model is a flow of gradient type, but adding a…

Dynamical Systems · Mathematics 2018-11-14 Jared Bronski , Thomas Carty , Lee DeVille

The Kuramoto model is a canonical model for understanding phase-locking phenomenon. It is well-understood that, in the usual mean-field scaling, full phase-locking is unlikely and that it is partially phase-locked states that are important…

Adaptation and Self-Organizing Systems · Physics 2021-06-30 Jared Bronski , Lan Wang

Model reduction techniques have been widely used to study the collective behavior of globally coupled oscillators. However, most approaches assume that there are infinitely many oscillators. Here we propose a new ansatz, based on the…

Adaptation and Self-Organizing Systems · Physics 2020-08-10 Lachlan D Smith , Georg A Gottwald

We consider the Kuramoto model on a graph with nodes given by $n$ i.i.d. points uniformly distributed on the $d$ dimensional torus. Two nodes are declared neighbors if they are at distance less than $\epsilon$. We prove a scaling limit for…

Probability · Mathematics 2025-06-03 Francisco Cirelli , Pablo Groisman , Ruojun Huang , Hernán Vivas

We study the synchronization of a generalized Kuramoto system in which the coupling weights are determined by the phase differences between oscillators. We employ the fast-learning regime in a Hebbian-like plasticity rule so that the…

Analysis of PDEs · Mathematics 2021-06-29 Jinyeong Park , David Poyato , Juan Soler

The Kuramoto model, which serves as a paradigm for investigating synchronization phenomenon of oscillatory system, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here, we generalize…

Adaptation and Self-Organizing Systems · Physics 2020-11-04 Can Xu , Xuebin Wang , Per Sebastian Skardal

Real world systems comprised of coupled oscillators have the ability to exhibit spontaneous synchronization and other complex behaviors. The interplay between the underlying network topology and the emergent dynamics remains a rich area of…

Pattern Formation and Solitons · Physics 2024-06-19 Monica Goebel , Matthew S Mizuhara , Sofia Stepanoff

The celebrated 1975 Kuramoto model of $N$ identical oscillators with phase angle vector $\boldsymbol{\vartheta}=(\vartheta_1,\ldots,\vartheta_N)$ and all-to-all coupling reads \begin{equation} \label{*}…

Dynamical Systems · Mathematics 2025-12-03 Jia-Yuan Dai , Bernold Fiedler , Alejandro López-Nieto

The exponential synchronization rate is addressed for Kuramoto oscillators in the presence of a pacemaker. When natural frequencies are identical, we prove that synchronization can be ensured even when the phases are not constrained in an…

Systems and Control · Computer Science 2012-09-06 Yongqiang Wang , Francis J. Doyle

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

We consider ensembles of sine-coupled phase oscillators consisting of subpopulations of identical units, with a general heterogeneous coupling between subpopulations. Using the Watanabe-Strogatz ansatz we reduce the dynamics of the ensemble…

Adaptation and Self-Organizing Systems · Physics 2010-01-11 Arkady Pikovsky , Michael Rosenblum

We study the dynamics of the large N limit of the Kuramoto model of coupled phase oscillators, subject to white noise. We introduce the notion of shadow inertial manifold and we prove their existence for this model, supporting the fact that…

Adaptation and Self-Organizing Systems · Physics 2015-05-28 Giambattista Giacomin , Khashayar Pakdaman , Xavier Pellegrin

We explore the collective phase dynamics of Wien-bridge oscillators coupled resistively. We carefully analyze the behavior of two coupled oscillators, obtaining a transformation from voltage to effective phase. From the phase dynamics we…

Adaptation and Self-Organizing Systems · Physics 2015-12-09 Lars Q. English , Zhuwei Zeng , David Mertens