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Synchronization is a fundamental phenomenon in complex systems, observed across a wide range of natural and engineered contexts. The Kuramoto model provides a foundational framework for understanding synchronization among coupled…

Adaptation and Self-Organizing Systems · Physics 2026-02-03 Riccardo Muolo , Hiroya Nakao , Marco Coraggio

We consider the problem of global synchronization in a large random network of Kuramoto oscillators where some of them are subject to an external periodically driven force. We explore a recently proposed dimensional reduction approach and…

Adaptation and Self-Organizing Systems · Physics 2019-07-31 Joyce S. Climaco , Alberto Saa

Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph…

Dynamical Systems · Mathematics 2022-08-25 Hardeep Bassi , Richard Yim , Rohith Kodukula , Joshua Vendrow , Cherlin Zhu , Hanbaek Lyu

The Kuramoto model, which describes synchronization phenomena, is a system of ordinary differential equations on $N$-torus defined as coupled harmonic oscillators. The order parameter is often used to measure the degree of synchronization.…

Dynamical Systems · Mathematics 2013-02-05 Hayato Chiba

Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…

Adaptation and Self-Organizing Systems · Physics 2024-08-23 Md Sayeed Anwar , S. Nirmala Jenifer , Paulsamy Muruganandam , Dibakar Ghosh , Timoteo Carletti

We study a generalized Kuramoto model in which each oscillator carries two coupled phase variables, representing a minimal swarmalator system. Assuming perfect correlation between the intrinsic frequencies associated with each phase…

Statistical Mechanics · Physics 2025-11-12 Hyunsuk Hong , Jae Sung Lee , Hyunggyu Park

The Kuramoto model is a system of ordinary differential equations for describing synchronization phenomena defined as a coupled phase oscillators. In this paper, a bifurcation structure of the infinite dimensional Kuramoto model is…

Dynamical Systems · Mathematics 2019-02-20 Hayato Chiba

We establish a unified synchronization framework for the all-to-all hybrid Kuramoto model that couples first- and second-order oscillators within a single dynamical system. Although the Kuramoto model has become one of the most widely used…

Dynamical Systems · Mathematics 2025-12-09 Ting-Yang Hsiao , Yun-Feng Lo , Chengbin Zhu

Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all…

Adaptation and Self-Organizing Systems · Physics 2015-11-18 Can Xu , Yuting Sun , Jian Gao , Tian Qiu , Zhigang Zheng , Shuguang Guan

In this paper we study cluster synchronization in networks of oscillators with heterogenous Kuramoto dynamics, where multiple groups of oscillators with identical phases coexist in a connected network. Cluster synchronization is at the…

Optimization and Control · Mathematics 2020-05-06 Tommaso Menara , Giacomo Baggio , Danielle S. Bassett , Fabio Pasqualetti

The self-consistent method, first introduced by Kuramoto, is a powerful tool for the analysis of the steady states of coupled oscillator networks. For second-order oscillator networks complications to the application of the self-consistent…

Adaptation and Self-Organizing Systems · Physics 2018-10-08 Jian Gao , Konstantinos Efstathiou

The Kuramoto model serves as a paradigm to study the phenomenon of spontaneous collective synchronization. We study here a nontrivial generalization of the Kuramoto model by including an interaction that breaks explicitly the rotational…

Adaptation and Self-Organizing Systems · Physics 2020-09-30 V K Chandrasekar , M Manoranjani , Shamik Gupta

In this paper, we study the convergence to the stable equilibrium for Kuramoto oscillators. Specifically, we derive estimates on the rate of convergence to the global equilibrium for solutions of the Kuramoto-Sakaguchi equation in a large…

Analysis of PDEs · Mathematics 2024-06-21 Javier Morales , David Poyato

While considerable progress has been made in the analysis of large systems containing a single type of coupled dynamical component (e.g., coupled oscillators or coupled switches), systems containing diverse components (e.g., both…

Chaotic Dynamics · Physics 2015-06-16 Dane Taylor , Elana J. Fertig , Juan G. Restrepo

We study synchronization patterns in repulsively coupled Kuramoto oscillators and focus on the impact of disorder in the natural frequencies. Among other choices we select the grid size and topology in a way that we observe a dynamically…

Adaptation and Self-Organizing Systems · Physics 2017-05-12 Darka Labavic , Hildegard Meyer-Ortmanns

Model reduction techniques have been widely used to study the collective behavior of globally coupled oscillators. However, most approaches assume that there are infinitely many oscillators. Here we propose a new ansatz, based on the…

Adaptation and Self-Organizing Systems · Physics 2020-08-10 Lachlan D Smith , Georg A Gottwald

We have studied two specific models of frustrated and disordered coupled Kuramoto oscillators, all driven with the same natural frequency, in the presence of random external pinning fields. Our models are structurally similar, but differ in…

Disordered Systems and Neural Networks · Physics 2009-11-07 ACC Coolen , C Perez-Vicente

The Kuramoto model captures various synchronization phenomena in biological and man-made systems of coupled oscillators. It is well-known that there exists a critical coupling strength among the oscillators at which a phase transition from…

Dynamical Systems · Mathematics 2011-05-06 Florian Dorfler , Francesco Bullo

Synchronization in a frequency-weighted Kuramoto model with a uniform frequency distribution is studied. We plot the bifurcation diagram and identify the asymptotic coherent states. Numerical simulations show that the system undergoes two…

Adaptation and Self-Organizing Systems · Physics 2017-03-01 Hongjie Bi , Yan Li , Li Zhou , Shuguang Guan

From biology to social science, the functioning of a wide range of systems is the result of elementary interactions which involve more than two constituents, so that their description has unavoidably to go beyond simple…

Adaptation and Self-Organizing Systems · Physics 2021-04-28 X. Dai , K. Kovalenko , M. Molodyk , Z. Wang , X. Li , D. Musatov , A. M. Raigorodskii , K. Alfaro-Bittner , G. D. Cooper , G. Bianconi , S. Boccaletti