English
Related papers

Related papers: Efficient Quantum Algorithms for Higher-Order Coup…

200 papers

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

Phase balanced states are a highly under-explored class of solutions of the Kuramoto model and other coupled oscillator models on networks. So far, coupled oscillator research focused on phase synchronized solutions. Yet, global constraints…

Biological Physics · Physics 2019-05-29 Franz Kaiser , Karen Alim

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

Synchronisation of coupled oscillators is a ubiquitous phenomenon, occurring in topics ranging from biology and physics, to social networks and technology. A fundamental and long-time goal in the study of synchronisation has been to find…

Adaptation and Self-Organizing Systems · Physics 2018-07-25 Edward J. Hancock , Georg A. Gottwald

The Kuramoto model provides a prototypical framework to synchronization phenomena in interacting particle systems. Apart from full phase synchrony where all oscillators behave identically, identical Kuramoto oscillators with ring-like…

Dynamical Systems · Mathematics 2023-08-02 Christian Bick , Tobias Böhle , Christian Kuehn

The Kuramoto model is a dynamical system that models the interaction of coupled oscillators. There has been much work to effectively bound the number of equilibria to the Kuramoto model for a given network. By formulating the Kuramoto…

Algebraic Geometry · Mathematics 2024-09-26 Tianran Chen , Evgeniia Korchevskaia , Julia Lindberg

Recently, there has been significant advancement in the machine learning (ML) approach and its application to diverse systems ranging from complex to quantum systems. As one of such systems, a coupled-oscillators system exhibits intriguing…

Statistical Mechanics · Physics 2021-09-21 Je Ung Song , K. Choi , B. Kahng

We investigate synchronization in networks of Kuramoto oscillators with inertia. More specifically, we introduce a rewiring algorithm consisting basically in a {\em hill climb} scheme in which the edges of the network are swapped in order…

Adaptation and Self-Organizing Systems · Physics 2016-08-01 Rafael S. Pinto , Alberto Saa

Nature is pervaded with oscillatory dynamics. In networks of coupled oscillators patterns can arise when the system synchronizes to an external input. Hence, these networks provide processing and memory of input. We present a universal…

Machine Learning · Computer Science 2025-06-23 Thomas Geert de Jong , Hirofumi Notsu , Kohei Nakajima

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

Synchronization is observed in many natural systems, with examples ranging from neuronal activation to walking pedestrians. The models proposed by Winfree and Kuramoto stand as the classic frameworks for investigating these phenomena. The…

Physics and Society · Physics 2024-06-14 Guilherme S. Costa , Marcus A. M. de Aguiar

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 study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to incorporate three- and four-body interactions into the dynamics…

Adaptation and Self-Organizing Systems · Physics 2025-05-26 Guilherme S. Costa , Marcel Novaes , Ricardo Fariello , Marcus A. M. de Aguiar

Coupled oscillator networks underlie many biological systems, from cardiac cycles to circadian rhythms. Phase-reduced models such as the Kuramoto model have been widely used to study synchronization, but they typically assume that…

Dynamical Systems · Mathematics 2026-05-29 Naghmeh Akhavan , Ruby Kim

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

This paper presents a nonlinear control framework for steering networks of coupled oscillators toward desired phase-locked configurations. Inspired by brain dynamics, where structured phase differences support cognitive functions, the focus…

Systems and Control · Electrical Eng. & Systems 2025-04-28 Adnan Tahirovic

The Kuramoto model, which serves as a paradigm for investigating synchronization phenomenon of oscillatory system, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here, we generalize…

Adaptation and Self-Organizing Systems · Physics 2020-11-04 Can Xu , Xuebin Wang , Per Sebastian Skardal

We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the…

Adaptation and Self-Organizing Systems · Physics 2015-01-28 Celso Freitas , Elbert Macau , Arkady Pikovsky

Artificial neural networks and their applications in deep learning have recently made an incursion into the field of control. Deep learning techniques in control are often related to optimal control, which relies on Pontryagin maximum…

Optimization and Control · Mathematics 2025-01-15 Emmanuel Delaleau , Cédric Join , Michel Fliess

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