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We analyze mean-field models of synchronization of phase oscillators with singular couplings and subject to external random forces. They are related to the Kuramoto-Sakaguchi model. Their probability densities satisfy local partial…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 L. L. Bonilla , C. J. Perez-Vicente , F. Ritort , J. Soler

The Kuramoto model is a classical nonlinear ODE system designed to study synchronization phenomena. Each equation represents the phase of an oscillator and the coupling between them is determined by a graph. There is an increasing interest…

Probability · Mathematics 2025-10-02 Cecilia De Vita , Pablo Groisman , Ruojun Huang

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

We study dynamics of phase-differences (PDs) of coupled oscillators where both the intrinsic frequencies and the couplings vary in time. In case the coupling coefficients are all nonnegative, we prove that the PDs are asymptotically stable…

Dynamical Systems · Mathematics 2018-06-15 Wenlian Lu , Fatihcan M. Atay

We introduce a system of pulse coupled oscillators that can change both their phases and frequencies; and prove that when there is a separation of time scales between phase and frequency adjustment the system converges to exact synchrony on…

Neurons and Cognition · Quantitative Biology 2015-06-18 Joel Nishimura

We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter. A bifurcation analysis of the transition from fully synchronous…

Adaptation and Self-Organizing Systems · Physics 2015-05-27 Oleksandr Burylko , Arkady Pikovsky

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

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

Effects of synchronization in a system of two coupled oscillators with time-delayed feedback are investigated. Phase space of a system with time delay is infinite-dimensional. Thus, the picture of synchronization in such systems acquires…

Chaotic Dynamics · Physics 2014-05-06 Yulia P. Emelianova , Valeriy V. Emelyanov , Nikita M. Ryskin

The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost…

Adaptation and Self-Organizing Systems · Physics 2025-05-16 Seungjae Lee , Lucas Braun , Frieder Bönisch , Malte Schröder , Moritz Thümler , Marc Timme

We study the chaotic behavior of the synchronization phase transition in the Kuramoto model. We discuss the relationship with analogous features found in the Hamiltonian Mean Field (HMF) model. Our numerical results support the connection…

Statistical Mechanics · Physics 2016-09-08 G. Miritello , A. Pluchino , A. Rapisarda

We numerically study the celebrated Kuramoto model of identical oscillators arranged on the sites of a two-dimensional periodic square lattice and subject to nearest neighbor interactions and dichotomous noise. In the nonequilibrium…

Adaptation and Self-Organizing Systems · Physics 2021-08-04 Mrinal Sarkar

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

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

Understanding the mechanisms that govern collective synchronization is a paramount task in nonlinear dynamics. While higher-order (many-body) interactions have recently emerged as a powerful framework for capturing collective behaviors,…

Adaptation and Self-Organizing Systems · Physics 2025-12-19 Narumi Fujii , Keisuke Taga , Riccardo Muolo , Bob Rink , Hiroya Nakao

We consider a Kuramoto model for the dynamics of an excitable system consisting of two coupled active rotators. Depending on both the coupling strength and the noise, the two rotators can be in a synchronized or desynchronized state. The…

Pattern Formation and Solitons · Physics 2011-09-27 Sebastian F. Brandt , Axel Pelster , Ralf Wessel

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

In this paper, we study the complete synchronization of the Kuramoto model with general network containing a spanning tree, when the initial phases are distributed in an open half circle. As lack of uniform coercivity in general digraph, in…

Dynamical Systems · Mathematics 2021-07-15 Xiongtao Zhang , Tingting Zhu

Maintaining the stability of synchronization state is crucial for the functioning of many natural and artificial systems. In this study, we develop methods to optimize the synchronization stability of the Kuramoto model by minimizing the…

Optimization and Control · Mathematics 2017-01-18 Bo Li , K. Y. Michael Wong

Synchronization in a population of oscillators with hyperbolic chaotic phases is studied for two models. One is based on the Kuramoto dynamics of the phase oscillators and on the Bernoulli map applied to these phases. This system possesses…

Chaotic Dynamics · Physics 2020-11-24 Arkady Pikovsky