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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

The transition to synchrony in the Kuramoto model of globally coupled phase oscillators with a uniform distribution of natural frequencies is discontinuous. We extend the theory of this transition to the Kuramoto-Sakaguchi model, taking…

Adaptation and Self-Organizing Systems · Physics 2026-04-14 Arkady Pikovsky

The Kuramoto model is a paradigmatic model of collective synchronization in coupled oscillator systems. Although its mathematical properties have been extensively investigated, exact phase trajectories from arbitrary initial conditions have…

Adaptation and Self-Organizing Systems · Physics 2026-05-14 Keisuke Taga

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

Synchronization in networks of coupled oscillators is a widely studied topic with extensive scientific and engineering applications. In this paper, we study the frequency synchronization problem for networks of Kuramoto oscillators with…

Optimization and Control · Mathematics 2018-09-25 Saber Jafarpour , Elizabeth Y. Huang , Francesco Bullo

When modeling the classical Kuramoto model, one of the key features is the tendency to synchronize. Accordingly, the most well-adopted choice of the coupling function is the sine function. Due to the oddness of the sine function, the…

Dynamical Systems · Mathematics 2024-04-02 Chun-Hsiung Hsia , Chung-En Tsai

We propose an infinite Kuramoto model for a countably infinite set of Kuramoto oscillators and study its emergent dynamics for two classes of network topologies. For a class of symmetric and row(or column)-summable network topology, we show…

Dynamical Systems · Mathematics 2023-10-05 Seung-Yeal Ha , Euntaek Lee , Woojoo Shim

We study the noisy Kuramoto model for two interacting communities of oscillators, where we allow the interaction in and between communities to be positive or negative (but not zero). We find that, in the thermodynamic limit where the size…

Probability · Mathematics 2019-04-16 J. M. Meylahn

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

We propose a modification of the Kuramoto model to account for the effective change in the coupling constant among the oscillators, as suggested by some experiments on Josephson junction, laser arrays and mechanical systems, where the…

Statistical Mechanics · Physics 2007-05-23 G. Filatrella , N. F. Pedersen , K. Wiesenfeld

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

Now a standard in Nonlinear Sciences, the Kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phenomenology has been sketched in early works, the…

Analysis of PDEs · Mathematics 2018-12-18 Helge Dietert , Bastien Fernandez

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

There are numerous examples of studied real-world systems that can be described as dynamical systems characterized by individual phases and coupled in a network like structure. Within the framework of oscillatory models, much attention has…

Physics and Society · Physics 2021-01-29 Gemma Rosell-Tarragó , Albert Díaz-Guilera

Using a recently introduced linear reformulation of the Kuramoto model of self-synchronizing oscillator systems (arXiv:0704.1166), we study a new class of analytically solvable oscillator systems defined by a particular coupling scheme. We…

Statistical Mechanics · Physics 2008-12-11 David C. Roberts , Razvan Teodorescu

A two-time scale asymptotic method has been introduced to analyze the multimodal mean-field Kuramoto-Sakaguchi model of oscillator synchronization in the high-frequency limit. The method allows to uncouple the probability density in…

patt-sol · Physics 2009-10-30 J. A. Acebron , L. L. Bonilla

Higher-order networks with multiway interactions can exhibit collective dynamical phenomena that are absent in traditional pairwise network models. However, analyzing such dynamics becomes computationally prohibitive as their state space…

Quantum Physics · Physics 2026-04-23 Caesnan M. G. Leditto , Angus Southwell , Muhammad Usman , Kavan Modi

The Kuramoto model is a classical model used in the study of spontaneous synchronizations in networks of coupled oscillators. In this model, frequency synchronization configurations can be formulated as complex solutions to a system of…

Algebraic Geometry · Mathematics 2019-12-16 Tianran Chen , Evgeniia Korchevskaia

Synchronization is a ubiquitous phenomenon in complex systems. The Kuramoto model serves as a paradigmatic framework for understanding how coupled oscillators achieve collective rhythm. Conventional approaches focus on pairwise…

Adaptation and Self-Organizing Systems · Physics 2026-03-16 Zheng Wang , Jinjie Zhu , Xianbin Liu

We analyze populations of Kuramoto oscillators with a particular distribution of natural frequencies. Inspired by networks where there are two groups of nodes with opposite behaviors, as for instance in power-grids where energy is either…

Pattern Formation and Solitons · Physics 2012-03-14 Lubos Buzna , Sergi Lozano , Albert Diaz-Guilera