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Coordination is ubiquitous in living systems. Existing theoretical models of coordination -- from bacteria to brains -- focus on either gross statistics in large-scale systems ($N\rightarrow\infty$) or detailed dynamics in small-scale…

Biological Physics · Physics 2019-08-16 Mengsen Zhang , Christopher Beetle , J. A. Scott Kelso , Emmanuelle Tognoli

After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: deterministic coupling and common forcing. The inclusion of independent random forcing in these models typically…

Adaptation and Self-Organizing Systems · Physics 2023-03-31 Jeremy Worsfold , Tim Rogers

The Kuramoto model was recently extended to arbitrary dimensions by reinterpreting the oscillators as particles moving on the surface of unit spheres in a D-dimensional space. Each particle is then represented by a D-dimensional unit…

Chaotic Dynamics · Physics 2023-04-21 Marcus A. M. de Aguiar

We study synchronization of Kuramoto oscillators in strongly modular networks in which the structure of the network inside each community is averaged. We find that the dynamics of the interacting communities can be described as an ensemble…

Adaptation and Self-Organizing Systems · Physics 2012-06-19 Per Sebastian Skardal , Juan G. Restrepo

Synchronization systems with effective inertia, such as power grid networks and coupled electromechanical oscillators, are commonly modeled by the second-order Kuramoto model. In the forward process, numerical simulations exhibit a…

Physics and Society · Physics 2026-04-01 Gug Young Kim , Mi Jin Lee , Seung-Woo Son

We consider a variant of the Kuramoto model, in which all the oscillators are now assumed to have the same natural frequency, but some of them are negatively coupled to the mean field. These "contrarian" oscillators tend to align in…

Chaotic Dynamics · Physics 2015-05-30 Hyunsuk Hong , Steven H. Strogatz

In order to discover generic effects of heterogeneous communication delays on the dynamics of large systems of coupled oscillators, this paper studies a modification of the Kuramoto model incorporating a distribution of interaction delays.…

Chaotic Dynamics · Physics 2009-05-06 Wai Shing Lee , Edward Ott , Thomas M. Antonsen

We examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can…

Adaptation and Self-Organizing Systems · Physics 2017-10-09 Jordan Snyder , Anatoly Zlotnik , Aric Hagberg

The Kuramoto model describes synchronization behavior among coupled oscillators and enjoys successful application in a wide variety of fields. Many of these applications seek phase-coherent solutions, i.e., equilibria of the model.…

Optimization and Control · Mathematics 2017-10-30 Owen Coss , Jonathan D. Hauenstein , Hoon Hong , Daniel K. Molzahn

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

The Kuramoto model, originally proposed to model the dynamics of many interacting oscillators, has been used and generalized for a wide range of applications involving the collective behavior of large heterogeneous groups of dynamical units…

Adaptation and Self-Organizing Systems · Physics 2019-01-09 Sarthak Chandra , Michelle Girvan , Edward Ott

We study the onset of synchronization in lattices of limit cycle oscillators with long-range coupling by means of numerical simulations. In this regime the critical coupling strength depends on the system size and interaction range…

Statistical Mechanics · Physics 2009-11-07 M. S. O. Massunaga , M. Bahiana

We consider the optimal experimental design problem for an uncertain Kuramoto model, which consists of N interacting oscillators described by coupled ordinary differential equations. The objective is to design experiments that can…

Optimization and Control · Mathematics 2021-05-04 Youngjoon Hong , Bongsuk Kwon , Byung-Jun Yoon

Synchronization is a ubiquitous phenomenon in nature. Although it is necessary for the functioning of many systems, too much synchronization can also be detrimental, e.g., (partially) synchronized brain patterns support high-level cognitive…

Dynamical Systems · Mathematics 2025-03-27 Martin Moriamé , Maxime Lucas , Timoteo Carletti

We generalize the Kuramoto model for the synchronization transition of globally coupled phase oscillators to populations by incorporating an additional heterogeneity with the coupling strength, where each oscillator pair interacts with…

Adaptation and Self-Organizing Systems · Physics 2016-12-21 Can Xu , Jian Gao , Hairong Xiang , Wenjing Jia , Shuguang Guan , Zhigang Zheng

Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…

Adaptation and Self-Organizing Systems · Physics 2015-08-19 Jason Hindes , Christopher R. Myers

We study Kuramoto phase oscillators with temporal fluctuations in the frequencies. The infinite-dimensional system can be reduced in a Gaussian approximation to two first-order differential equations. This yields a solution for the…

Statistical Mechanics · Physics 2013-11-12 Bernard Sonnenschein , Lutz Schimansky-Geier

The Kuramoto model with higher-order interactions has recently been shown to exhibit bistability, explosive synchronization transitions, and rich collective dynamics. Existing analytical approaches, however, typically rely on all-to-all…

Adaptation and Self-Organizing Systems · Physics 2026-05-26 Chanin Kumpeerakij , Juan G. Restrepo

The Kuramoto model of coupled phase oscillators is often used to describe synchronization phenomena in nature. Some applications, e.g., quantum synchronization and rigid-body attitude synchronization, involve high-dimensional Kuramoto…

Optimization and Control · Mathematics 2022-03-15 Johan Markdahl , Johan Thunberg , Jorge Goncalves

In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others…

Statistical Mechanics · Physics 2009-11-10 Yamir Moreno , Amalio F. Pacheco