English
Related papers

Related papers: The Kuramoto model in complex networks

200 papers

Synchronization in networks of coupled oscillators is classically studied via the Kuramoto model, whose intrinsic nonlinearity limits analytical tractability and complicates control design. Complex-valued extensions circumvent this by…

Systems and Control · Electrical Eng. & Systems 2026-04-09 Lorenzo Giordano , Josep M. Olm , Mario di Bernardo

We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent…

Chaotic Dynamics · Physics 2015-06-19 M. Komarov , A. Pikovsky

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

In this work we study the dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution. Synchronization is achieved after a threshold…

Physics and Society · Physics 2015-10-28 R. K. Singh , Trilochan Bagarti

The Kuramoto model has provided deep insights into synchronization phenomena and remains an important paradigm to study the dynamics of coupled oscillators. Yet, despite its success, the asynchronous regime in the Kuramoto model has…

Mathematical Physics · Physics 2024-03-26 Yagmur Kati , Jonas Ranft , Benjamin Lindner

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 consider a long-range model of coupled phase-only oscillators subject to a local potential and evolving in presence of thermal noise. The model is a non-trivial generalization of the celebrated Kuramoto model of collective…

Adaptation and Self-Organizing Systems · Physics 2017-01-04 Alessandro Campa , Shamik Gupta

Due to its description of a synchronization between oscillators, the Kuramoto model is an ideal choice for a synchronisation algorithm in networked systems. This requires to achieve not only a frequency synchronization but also a phase…

Systems and Control · Electrical Eng. & Systems 2024-03-21 Andreas Bathelt , Vimukthi Herath , Thomas Dallmann

Many real-world systems of coupled agents exhibit directed interactions, meaning that the influence of an agent on another is not reciprocal. Furthermore, interactions usually do not have identical amplitude and/or sign. To describe…

Adaptation and Self-Organizing Systems · Physics 2019-08-13 Robin Delabays , Philippe Jacquod , Florian Dörfler

Synchronizing phase frustrated Kuramoto oscillators, a challenge that has found applications from neuronal networks to the power grid, is an eluding problem, as even small phase-lags cause the oscillators to avoid synchronization. Here we…

Adaptation and Self-Organizing Systems · Physics 2018-01-19 Prosenjit Kundu , Chittaranjan Hens , Baruch Barzel , Pinaki Pal

We examine a modification of the Kuramoto model for phase oscillators coupled on a network. Here, two populations of oscillators are considered, each with different network topologies, internal and cross-network couplings and frequencies.…

Dynamical Systems · Mathematics 2016-02-17 A. C. Kalloniatis , M. L. Zuparic

We introduce a novel coupling scheme for maximizing the synchronization of Kuramoto oscillator networks under a fixed coupling budget. We show that by scaling the interaction strength between oscillators according to their frequency…

Statistical Mechanics · Physics 2026-04-01 Amit Pando , Eran Bernstein , Tomer Hacohen , Nathan Vigne , Hui Cao , Oren Raz , Asher Friesem , Nir Davidson

Kuramoto's differential equation describes a synchronization process between several harmonic oscillators. It has been used to model biological phenomena such as the synchronization of heart cells, the circadian rhythm, or brain waves. It…

Dynamical Systems · Mathematics 2026-05-26 Daniel Burns , Gregorio Malajovich , Charles Pugh , Indika Rajapakse , Steve Smale

In this paper, we study the synchronization of identical Kuramoto phase oscillators under cumulative stochastic damage to the edges of networks. We analyze the capacity of coupled oscillators to reach a coherent state from initial random…

Statistical Mechanics · Physics 2023-10-31 Leidy Katherin Eraso Hernández , Alejandro P. Riascos

Populations of oscillators are present throughout nature. Very often synchronization is observed in such populations if they are allowed to interact. A paradigmatic model for the study of such phenomena has been the Kuramoto model. However,…

Adaptation and Self-Organizing Systems · Physics 2022-06-08 Keith A. Kroma-Wiley , Peter J. Mucha , Dani S. Bassett

The dynamics of large systems of coupled oscillators is a subject of increasing importance with prominent applications in several areas such as physics and biology. The Kuramoto model, where a set of oscillators move around a circle…

Adaptation and Self-Organizing Systems · Physics 2021-11-24 Ana Elisa D. Barioni , Marcus A. M. de Aguiar

We generalize the Kuramoto model of coupled oscillators to allow time-delayed interactions. New phenomena include bistability between synchronized and incoherent states, and unsteady solutions with time-dependent order parameters. We derive…

chao-dyn · Physics 2009-10-31 M. K. Stephen Yeung , Steven H. Strogatz

A new collective behavior of resonant synchronization is discovered and the ability to retrieve information from brain memory is proposed based on this mechanism. We use modified Kuramoto phase oscillator to simulate the dynamics of a…

Adaptation and Self-Organizing Systems · Physics 2018-09-06 Lin Zhang , Xv Li , Tingting Xue

We study the emergence of synchronization in the Kuramoto model on a digraph in the presence of time delays. Assuming the digraph is strongly connected, we first establish a uniform bound on the phase diameter and subsequently prove the…

Optimization and Control · Mathematics 2024-06-05 Conor Carty , Young-Pil Choi , Chiara Cicolani , Cristina Pignotti

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