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Related papers: On the Critical Coupling for Kuramoto Oscillators

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By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…

Networking and Internet Architecture · Computer Science 2024-11-20 Agostino Funel

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

Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…

Adaptation and Self-Organizing Systems · Physics 2021-11-01 Can Xu , Xiaohuan Tang , Huaping Lü , Karin Alfaro-Bittner , Stefano Boccaletti , Matjaz Perc , Shuguang Guan

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

We study the synchronization of oscillators with inertias and phase shifts, namely the second-order Kuramoto-Sakaguchi model. Using the self-consistent method, we find that the effect of inertia is the introduction of effective phase…

Adaptation and Self-Organizing Systems · Physics 2020-12-29 Jian Gao , Konstantinos Efstathiou

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 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

Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously…

Adaptation and Self-Organizing Systems · Physics 2018-08-23 Stefano Gherardini , Shamik Gupta , Stefano Ruffo

We investigate synchronization in a Kuramoto-like model with nearest neighbour coupling. Upon analyzing the behaviour of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the…

The Kuramoto model is a standard model for the dynamics of coupled oscillator networks. In particular, it is used to study long time behavior such as phase-locking where all oscillators rotate at a common frequency with fixed angle…

Dynamical Systems · Mathematics 2020-01-30 Timothy Ferguson

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

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

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 classical Kuramoto model consists of finitely many pairwise coupled oscillators on the circle. In many applications a simple pairwise coupling is not sufficient to describe real-world phenomena as higher-order (or group) interactions…

Dynamical Systems · Mathematics 2023-05-25 Christian Bick , Tobias Böhle , Christian Kuehn

We report finite size numerical investigations and mean field analysis of a Kuramoto model with inertia for fully coupled and diluted systems. In particular, we examine for a Gaussian distribution of the frequencies the transition from…

Disordered Systems and Neural Networks · Physics 2015-04-14 Simona Olmi , Adrian Navas , Stefano Boccaletti , Alessandro Torcini

An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…

Dynamical Systems · Mathematics 2014-05-13 Vishaal Krishnan , Arun D. Mahindrakar , Somashekhar S. Hiremath

We investigate hysteresis in a generalized Kuramoto model with identical oscillators, focusing on coupling strength inhomogeneity, which results in oscillators being coupled to others with varying strength, and a simplified, more realistic…

Dynamical Systems · Mathematics 2024-10-25 Jae Hyung Woo , Hae Seong Lee , Joon-Young Moon , Tae-Wook Ko

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 second-order Kuramoto equation describes synchronization of coupled oscillators with inertia, which occur in power grids for example. Contrary to the first-order Kuramoto equation it's synchronization transition behavior is much less…

Statistical Mechanics · Physics 2023-01-16 Géza Ódor , Shengfeng Deng

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