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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

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 (KM) of coupled phase oscillators on scale free graphs is analyzed in this work. The W-random graph model is used to define a convergent family of sparse graphs with power law degree distribution. For the KM on this…

Adaptation and Self-Organizing Systems · Physics 2017-05-16 Georgi S. Medvedev , Xuezhi Tang

The stochastic Kuramoto model defined on a sequence of graphs is analyzed: the emphasis is posed on the relationship between the mean field limit, the connectivity of the underlying graph and the long time behavior. We give an explicit…

Probability · Mathematics 2019-12-24 Fabio Coppini

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

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 present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic,…

Disordered Systems and Neural Networks · Physics 2009-11-11 Juan G. Restrepo , Edward Ott , Brian R. Hunt

The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The…

Adaptation and Self-Organizing Systems · Physics 2021-09-15 M. Manoranjani , Shamik Gupta , V. K. Chandrasekar

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

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

In our previous work [Chiba, Medvedev, arXiv:1612.06493], we initiated a mathematical investigation of the onset of synchronization in the Kuramoto model (KM) of coupled phase oscillators on convergent graph sequences. There, we derived and…

Dynamical Systems · Mathematics 2018-04-24 Hayato Chiba , Georgi S. Medvedev

This paper studies a mean field game formulation of the classical Kuramoto model for synchronization. Our model captures the diversity within the population by considering random intrinsic frequencies, which allows us to study the impact of…

Functional Analysis · Mathematics 2025-09-23 Rene Carmona , Quentin Cormier , Mete Soner

The Kuramoto model is fundamental to the study of synchronization. It consists of a collection of oscillators with interactions given by a network, which we identify respectively with vertices and edges of a graph. In this paper, we show…

The Kuramoto model, despite its popularity as a mean-field theory for many synchronization phenomenon of oscillatory systems, is limited to a first-order harmonic coupling of phases. For higher-order coupling, there only exists a…

Adaptation and Self-Organizing Systems · Physics 2020-01-22 Chen Chris Gong , Arkady Pikovsky

We analyse the collective behavior of a mean-field model of phase-oscillators of Kuramoto-Daido type coupled through pairwise interactions which depend on phase differences: the coupling function is composed of three harmonics. We provide…

Chaotic Dynamics · Physics 2021-01-05 Pau Clusella , Antonio Politi

In his classical work, Kuramoto analytically described the onset of synchronization in all-to-all coupled networks of phase oscillators with random intrinsic frequencies. Specifically, he identified a critical value of the coupling…

Dynamical Systems · Mathematics 2018-08-15 Hayato Chiba , Georgi S. Medvedev , Matthew S. Mizuhara

Kuramoto model is one of the most prominent models for the synchronization of coupled oscillators. It has long been a research hotspot to understand how natural frequencies, the interaction between oscillators, and network topology…

Adaptation and Self-Organizing Systems · Physics 2020-04-08 Shuyang Ling

We propose the Kuramoto Graph Neural Network (KuramotoGNN), a novel class of continuous-depth graph neural networks (GNNs) that employs the Kuramoto model to mitigate the over-smoothing phenomenon, in which node features in GNNs become…

Machine Learning · Computer Science 2024-03-07 Tuan Nguyen , Hirotada Honda , Takashi Sano , Vinh Nguyen , Shugo Nakamura , Tan M. Nguyen

A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of limit-cycle oscillators of distributed frequencies that are globally coupled…

Adaptation and Self-Organizing Systems · Physics 2020-09-08 Mrinal Sarkar , Shamik Gupta

Synaptic plasticity is a key component of neuronal dynamics, describing the process by which the connections between neurons change in response to experiences. In this study, we extend a network model of $\theta$-neuron oscillators to…

Neurons and Cognition · Quantitative Biology 2024-08-01 Niamh Fennelly , Alannah Neff , Renaud Lambiotte , Andrew Keane , Áine Byrne