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We study the emergence of synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and a time delay is…

Statistical Mechanics · Physics 2012-03-07 Thomas Kauê Dal'Maso Peron , Francisco Aparecido Rodrigues

We consider a Kuramoto model of coupled oscillators that includes quenched random interactions of the type used by van Hemmen in his model of spin glasses. The phase diagram is obtained analytically for the case of zero noise and a…

Chaotic Dynamics · Physics 2015-06-17 Isabel M. Kloumann , Ian M. Lizarraga , Steven H. Strogatz

The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N…

Neurons and Cognition · Quantitative Biology 2015-05-14 Lorenzo Bertini , Giambattista Giacomin , Khashayar Pakdaman

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

Coupled nonlinear oscillators, e.g., Kuramoto models, are commonly used to analyze electrical power systems. The cage model from statistical mechanics has also been used to describe the dynamics of synchronously connected generation…

Systems and Control · Electrical Eng. & Systems 2019-08-14 Marios Zarifakis , Declan J. Byrne , William T. Coffey , Yuri P. Kalmykov , Serguey V. Titov , Stephen J. Carrig

Many real-world systems of coupled agents exhibit directed interactions, meaning that the influence of an agent on another is not reciprocal. Furthermore, interactions usually do not have identical amplitude and/or sign. To describe…

Adaptation and Self-Organizing Systems · Physics 2019-08-13 Robin Delabays , Philippe Jacquod , Florian Dörfler

We study synchronization properties of coupled oscillators on networks that allow description in terms of global mean field coupling. These models generalize the standard Kuramoto-Sakaguchi model, allowing for different contributions of…

Chaotic Dynamics · Physics 2015-06-19 Vladimir Vlasov , Elbert E. N. Macau , Arkady Pikovsky

The Kuramoto model is a versatile mathematical framework that explains phenomena resulting from interactions among phase oscillators. It finds applications in various scientific and engineering domains. In this study, we focused on a…

Chaotic Dynamics · Physics 2023-06-28 Mohammad Javad Nouhi , Javad Noorbakhsh

We present a collective coordinate approach to describe coupled phase oscillators. We apply the method to study synchronisation in a Kuramoto model. In our approach an N-dimensional Kuramoto model is reduced to an n-dimensional ordinary…

Pattern Formation and Solitons · Physics 2015-05-21 Georg A. Gottwald

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

The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and…

Statistical Mechanics · Physics 2009-11-13 Hyunsuk Hong , Hyunggyu Park , Lei-Han Tang

We study the phase diagram of a generalized Winfree model. The modification is such that the coupling depends on the fraction of synchronized oscillators, a situation which has been noted in some experiments on coupled Josephson junctions…

Disordered Systems and Neural Networks · Physics 2008-07-25 F. Giannuzzi , D. Marinazzo , G. Nardulli , M. Pellicoro , S. Stramaglia

We study bifurcations of the completely synchronized state in a continuum limit (CL) for the Kuramoto model (KM) of identical oscillators with two-mode interaction depending on two graphs. Here one of the graphs is uniform but may be…

Dynamical Systems · Mathematics 2025-08-20 Kazuyuki Yagasaki

In this work, we analyze the Kuramoto model (KM) with inertia on a convergent family of graphs. It is assumed that the intrinsic frequencies of the individual oscillators are sampled from a probability distribution. In addition, a given…

Pattern Formation and Solitons · Physics 2023-07-26 Hayato Chiba , Georgi S. Medvedev , Matthew S. Mizuhara

We study bifurcations of twisted solutions in a continuum limit (CL) for the Kuramoto model (KM) of identical oscillators defined on nearest neighbor graphs, which may be deterministic dense, random dense or random sparse, when it may have…

Dynamical Systems · Mathematics 2026-01-06 Kazuyuki Yagasaki

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

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

Kuramoto oscillators are widely used to explain collective phenomena in networks of coupled oscillatory units. We show that simple networks of two populations with a generic coupling scheme, where both coupling strengths and phase lags…

Chaotic Dynamics · Physics 2018-07-20 Christian Bick , Mark J. Panaggio , Erik A. Martens

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

In this paper, we study the complete synchronization of the Kuramoto model with general network containing a spanning tree, when the initial phases are distributed in an open half circle. As lack of uniform coercivity in general digraph, in…

Dynamical Systems · Mathematics 2021-07-15 Xiongtao Zhang , Tingting Zhu