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Synchronization in coupled oscillators networks is a remarkable phenomenon of relevance in numerous fields. For Kuramoto oscillators the loss of synchronization is determined by a trade-off between coupling strength and oscillator…

Optimization and Control · Mathematics 2018-07-27 Saber Jafarpour , Francesco Bullo

We consider a mean-field model of coupled phase oscillators with quenched disorder in the natural frequencies and coupling strengths. A fraction $p$ of oscillators are positively coupled, attracting all others, while the remaining fraction…

Statistical Mechanics · Physics 2016-11-03 Hyunsuk Hong , Kevin P. O'Keeffe , Steven H. Strogatz

We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic,…

Disordered Systems and Neural Networks · Physics 2009-11-11 Juan G. Restrepo , Edward Ott , Brian R. Hunt

Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to…

Optimization and Control · Mathematics 2011-06-28 Florian Dorfler , Francesco Bullo

The asymptotic scaling behavior of the Kuramoto model with finite populations has been notably elusive, despite comprehensive investigations employing both analytical and numerical methods. In this paper, we explore the Kuramoto model with…

Statistical Mechanics · Physics 2024-09-30 Su-Chan Park , Hyunggyu Park

We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary…

Optimization and Control · Mathematics 2007-05-23 Ali Jadbabaie , Nader Motee , Mauricio Barahona

Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only…

Adaptation and Self-Organizing Systems · Physics 2019-11-11 Yury Sokolov , G. Bard Ermentrout

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

Aiming at the core problem that it is difficult for a fixed inertia coefficient to balance transient disturbance suppression and long-term stability in complex network synchronization systems, an adaptive inertia control strategy based on…

Systems and Control · Electrical Eng. & Systems 2026-01-22 Yiwei Zhou , Zhongcheng Lei , Xiaoran Dai , Wenshan Hu , Hong Zhou

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

We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, $N\to\infty$. This model is distinguished by dense multistability, where multiple states coexist for the same system parameters. The…

Adaptation and Self-Organizing Systems · Physics 2024-11-12 Rok Cestnik , Erik A. Martens

We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…

Adaptation and Self-Organizing Systems · Physics 2020-05-29 David Métivier , Lucas Wetzel , Shamik Gupta

We investigate transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto (SK) model on complex networks both analytically and numerically. We analytically derive self-consistent equations for group angular velocity and order…

Adaptation and Self-Organizing Systems · Physics 2017-11-29 Prosenjit Kundu , Pitambar Khanra , Chittaranjan Hens , Pinaki Pal

A fundamental understanding of synchronized behavior in multi-agent systems can be acquired by studying analytically tractable Kuramoto models. However, such models typically diverge from many real systems whose dynamics evolve under…

Adaptation and Self-Organizing Systems · Physics 2021-07-28 Keith A. Wiley , Peter J. Mucha , Danielle S. Bassett

We study the emergence of synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and a time delay is…

Statistical Mechanics · Physics 2012-03-07 Thomas Kauê Dal'Maso Peron , Francisco Aparecido Rodrigues

A two-dimensional lattice of oscillators with identical (zero) intrinsic frequencies and Kuramoto type of interactions with randomly frustrated couplings is considered. Starting the time evolution from slightly perturbed synchronized…

Disordered Systems and Neural Networks · Physics 2025-05-06 Róbert Juhász , Géza Ódor

Synchronization commonly occurs in many natural and man-made systems, from neurons in the brain to cardiac cells to power grids to Josephson junction arrays. Transitions to or out of synchrony for coupled oscillators depend on several…

Adaptation and Self-Organizing Systems · Physics 2018-05-10 Hui Wu , Mukesh Dhamala

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

The Kuramoto model is one of the most widely studied model for describing synchronization behaviors in a network of coupled oscillators, and it has found a wide range of applications. Finding all possible frequency synchronization…

Combinatorics · Mathematics 2019-09-04 Tianran Chen

The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…

Disordered Systems and Neural Networks · Physics 2013-05-30 Luce Prignano , Albert Diaz Guilera