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Related papers: Finite-size effects in a stochastic Kuramoto model

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The Kuramoto model, a paradigmatic framework for studying synchronization, exhibits a transition to collective oscillations only above a critical coupling strength in the thermodynamic limit. However, real-world systems are finite, and…

Chaotic Dynamics · Physics 2025-06-30 Sergei Kirillov , Vladimir Klinshov

Finite-size systems of Kuramoto model display intricate dynamics, especially in the presence of multi-stability where both coherent and incoherent states coexist. We investigate such scenario in globally coupled populations of Kuramoto…

Adaptation and Self-Organizing Systems · Physics 2024-05-28 Ayushi Suman , Sarika Jalan

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 present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this…

Adaptation and Self-Organizing Systems · Physics 2018-04-04 Franziska Peter , Arkady Pikovsky

We investigate the finite-size effects on the dynamical evolution of the Kuramoto model with inertia coupled through triadic interactions. Our findings reveal that fluctuations resulting from the finite size drive the system toward a…

Adaptation and Self-Organizing Systems · Physics 2025-07-01 Manuel Lourenco , Abhishek Sharma , Priyanka Rajwani , Erick Alejandro Madrigal Solis , Mehrnaz Anvari , Sarika Jalan

Super-critical Kuramoto oscillators with distributed frequencies separate into two disjoint groups: an ordered one locked to the mean field, and a disordered one consisting of effectively decoupled oscillators -- at least so in the…

Adaptation and Self-Organizing Systems · Physics 2019-09-18 F. Peter , C. Gong , A. Pikovsky

We perform a stochastic model reduction of the Kuramoto-Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators exhibit stationary states and a constant…

Adaptation and Self-Organizing Systems · Physics 2024-05-14 Wenqi Yue , Georg A. Gottwald

Synchronization transition in oscillatory networks manifests itself as the appearance of a periodic global mode. While perfect in the thermodynamic limit, this mode fluctuates for finite ensembles. We characterize the coherence of this mode…

Chaotic Dynamics · Physics 2026-01-12 A. Pikovsky , F. Bagnoli , S. Iubini

We study the emergent collective behaviors for an ensemble of identical Kuramoto oscillators under the effect of inertia. In the absence of inertial effects, it is well known that the generic initial Kuramoto ensemble relaxes to the…

Dynamical Systems · Mathematics 2017-07-25 Young-Pil Choi , Seung-Yeal Ha , Javier Morales

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

We investigate the diffusion coefficient of the time integral of the Kuramoto order parameter in globally coupled nonidentical phase oscillators. This coefficient represents the deviation of the time integral of the order parameter from its…

Chaotic Dynamics · Physics 2012-04-03 Isao Nishikawa , Gouhei Tanaka , Takehiko Horita , Kazuyuki Aihara

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

Phase transitions, sharp in the thermodynamic limit, get smeared in finite systems where macroscopic order-parameter fluctuations dominate. Achieving a coherent and complete theoretical description of these fluctuations is a central…

Statistical Mechanics · Physics 2025-10-06 Rupak Majumder , Julien Barré , Shamik Gupta

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

The Kuramoto-Sakaguchi model for coupled phase oscillators with phase-frustration is often studied in the thermodynamic limit of infinitely many oscillators. Here we extend a model reduction method based on collective coordinates to capture…

Adaptation and Self-Organizing Systems · Physics 2020-07-01 Wenqi Yue , Lachlan D. Smith , Georg A. Gottwald

Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behaviour, such as frequency synchronisation (FS) as a paradigm, in real-world networks with a finite number of oscillators.…

Adaptation and Self-Organizing Systems · Physics 2015-09-15 Chengwei Wang , Nicolas Rubido , Celso Grebogi , Murilo S. Baptista

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

Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously…

Adaptation and Self-Organizing Systems · Physics 2018-08-23 Stefano Gherardini , Shamik Gupta , Stefano Ruffo

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 entrainment transition of coupled random frequency oscillators presents a long-standing problem in nonlinear physics. The onset of entrainment in populations of large but finite size exhibits strong sensitivity to fluctuations in the…

Chaotic Dynamics · Physics 2015-05-20 Lei-Han Tang
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