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Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal…

Optimization and Control · Mathematics 2017-09-20 Lorenzo Tiberi , Chiara Favaretto , Mario Innocenti , Danielle S. Bassett , Fabio Pasqualetti

Disorder is often seen as detrimental to collective dynamics, yet recent work has shown that heterogeneity can enhance network synchronization. However, its constructive role in stabilizing nontrivial cooperative patterns remains largely…

Kuramoto oscillators have been proposed earlier as a model for interacting systems that exhibit synchronisation. In this article we study the difference between networks with symmetric and asymmetric distribution of natural frequencies. We…

Adaptation and Self-Organizing Systems · Physics 2014-12-22 Arindam Saha , R. E. Amritkar

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

We present an approach for the description of fluctuations that are due to finite system size induced correlations in the Kuramoto model of coupled oscillators. We construct a hierarchy for the moments of the density of oscillators that is…

Chaotic Dynamics · Physics 2009-11-11 Eric J. Hildebrand , Michael A. Buice , Carson C. Chow

Globally coupled phase oscillator models, such as the Kuramoto model, exhibit spontaneous collective synchronization. Such models can be restated in terms of interactions within and between subsets of oscillators. An approximation for the…

Adaptation and Self-Organizing Systems · Physics 2015-06-17 David Mertens

We study the bifurcations and phase diagram for a network of identical Kuramoto oscillators with a coupling that explicitly breaks the rotational symmetry of the equations. Applying the Watanabe-Strogatz ansatz, the original N-dimensional…

Chaotic Dynamics · Physics 2025-09-05 Antonio Mihara , Rene O. Medrano-T

Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior. It is interesting to ask how the structural organization of network interactions influences this process. Several…

Adaptation and Self-Organizing Systems · Physics 2017-09-13 Lia Papadopoulos , Jason Kim , Jurgen Kurths , Danielle S. Bassett

We consider the synchronization of oscillators in complex networks where there is an interplay between the oscillator dynamics and the network topology. Through a remarkable transformation in parameter space and the introduction of virtual…

Adaptation and Self-Organizing Systems · Physics 2020-04-22 Jian Gao , Konstantinos Efstathiou

The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the…

Adaptation and Self-Organizing Systems · Physics 2009-11-13 Michael A. Buice , Carson C. Chow

We investigate how correlations between the diversity of the connectivity of networks and the dynamics at their nodes affect the macroscopic behavior. In particular, we study the synchronization transition of coupled stochastic phase…

Disordered Systems and Neural Networks · Physics 2013-01-22 Bernard Sonnenschein , Francesc Sagués , Lutz Schimansky-Geier

We study patterns observed right after the loss of stability of mixing in the Kuramoto model of coupled phase oscillators with random intrinsic frequencies on large graphs, which can also be random. We show that the emergent patterns are…

Chaotic Dynamics · Physics 2020-09-02 Hayato Chiba , Georgi S. Medvedev , Matthew S. Mizuhara

In this paper, by extending the concept of Kuramoto oscillator to the left-invariant flow on general Lie group, we investigate the generalized phase synchronization on networks. The analyses and simulations of some typical dynamical systems…

Statistical Mechanics · Physics 2015-06-25 Zhi-Ming Gu , Ming Zhao , Tao Zhou , Chen-Ping Zhu , Bing-Hong Wang

We revisit the Kuramoto model to explore the finite-size scaling (FSS) of the order parameter and its dynamic fluctuations near the onset of the synchronization transition, paying particular attention to effects induced by the randomness of…

Statistical Mechanics · Physics 2015-08-26 Hyunsuk Hong , Hugues Chaté , Lei-Han Tang , Hyunggyu Park

In a large variety of systems (biological, physical, social etc.), synchronization occurs when different oscillating objects tune their rhythm when they interact with each other. The different underlying network defining the connectivity…

Adaptation and Self-Organizing Systems · Physics 2023-03-07 Juliette Courson , Thanos Manos , Mathias Quoy

Finite-size effects in the Kuramoto model are known to induce collective fluctuations even below the critical coupling, where the thermodynamic limit predicts complete asynchrony. While the shot-noise approach developed in our recent work…

Chaotic Dynamics · Physics 2026-03-31 S. Yu. Kirillov , V. V. Klinshov

The celebrated Ott-Antonsen ansatz for coupled oscillators provides a useful framework to work with deterministic systems in the thermodynamic limit, but remains just an approximation for stochastic models. In this paper, I construct a…

Statistical Mechanics · Physics 2024-07-03 Victor Buendía

The synchronization phenomena in thermoacoustic systems leading to oscillatory instability can effectively be modeled using Kuramoto oscillators. Such models consider the nonlinear response of flame as an ensemble of Kuramoto phase…

Chaotic Dynamics · Physics 2025-02-20 Rohan K. Nakade , Samarjeet Singh , Jayesh M. Dhadphale , R. I. Sujith

We consider the influence of correlated noise on the stability of synchronisation of oscillators on a general network using the Kuramoto model for coupled phases $\theta_i$. Near the fixed point $\theta_i \approx \theta_j \ \forall i,j$ the…

Statistical Mechanics · Physics 2013-04-29 Mathew Zuparic , Alexander C. Kalloniatis

We develop an approach for the description of the dynamics of large populations of phase oscillators based on "circular cumulants" instead of the Kuramoto-Daido order parameters. In the thermodynamic limit, these variables yield a simple…

Adaptation and Self-Organizing Systems · Physics 2018-07-04 Irina V. Tyulkina , Denis S. Goldobin , Lyudmila S. Klimenko , Arkady Pikovsky