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Related papers: Small-world networks of Kuramoto oscillators

200 papers

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 propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency…

Optimization and Control · Mathematics 2020-06-23 Regina S. Burachik , Alexander C. Kalloniatis , C. Yalçın Kaya

We study synchronization properties of coupled oscillators on networks that allow description in terms of global mean field coupling. These models generalize the standard Kuramoto-Sakaguchi model, allowing for different contributions of…

Chaotic Dynamics · Physics 2015-06-19 Vladimir Vlasov , Elbert E. N. Macau , Arkady Pikovsky

We study the Kuramoto-Sakaguchi (KS) model composed by any N identical phase oscillators symmetrically coupled. Ranging from local (one-to-one, R = 1) to global (all-to-all, R = N/2) couplings, we derive the general solution that describes…

Chaotic Dynamics · Physics 2018-05-04 Antonio Mihara , Rene O. Medrano-T

Oscillatory networks subjected to noise are broadly used to model physical and technological systems. Due to their nonlinear coupling, such networks typically have multiple stable and unstable states that a network might visit due to noise.…

Pattern Formation and Solitons · Physics 2026-01-27 Jason Hindes , Ira B. Schwartz , Melvyn Tyloo

We study the Kuramoto model on complex networks, in which natural frequencies of phase oscillators and the vertex degrees are correlated. Using the annealed network approximation and numerical simulations we explore a special case in which…

Disordered Systems and Neural Networks · Physics 2013-03-14 B. C. Coutinho , A. V. Goltsev , S. N. Dorogovtsev , J. F. F. Mendes

We consider an infinite network of globally-coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when…

Chaotic Dynamics · Physics 2015-05-30 Paul So , Ernest Barreto

We study bifurcations of twisted solutions in a continuum limit (CL) for the Kuramoto model (KM) of identical oscillators defined on nearest neighbor graphs, which may be deterministic dense, random dense or random sparse, when it may have…

Dynamical Systems · Mathematics 2026-01-06 Kazuyuki Yagasaki

Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…

Pattern Formation and Solitons · Physics 2026-02-27 Oleh E. Omel'chenko

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

Adaptive Kuramoto models admit a variety of nontrivial phase-locked configurations, including antipodal and rotating-wave states. A central open question is whether the observed persistence of such configurations can be attributed to…

Dynamical Systems · Mathematics 2026-02-13 Jaeyoung Yoon , Christian Kuehn

In networks of coupled oscillators, it is of interest to understand how interaction topology affects synchronization. Many studies have gained key insights into this question by studying the classic Kuramoto oscillator model on static…

Adaptation and Self-Organizing Systems · Physics 2020-09-29 William Qian , Lia Papadopoulos , Zhixin Lu , Keith Wiley , Fabio Pasqualetti , Danielle S. Bassett

Solitary states emerge in oscillator networks when one oscillator separates from the fully synchronized cluster and becomes incoherent with the rest of the network. Such chimera-type patterns with an incoherent state formed by a single…

Pattern Formation and Solitons · Physics 2022-03-02 V. O. Munyaev , M. I. Bolotov , L. A. Smirnov , G. V. Osipov , I. V. Belykh

We present a linear stability analysis of the incoherent state in a system of globally coupled, identical phase oscillators subject to colored noise. In that we succeed to bridge the extreme time scales between the formerly studied and…

Disordered Systems and Neural Networks · Physics 2015-05-18 Ralf Toenjes

The synchronization pattern of a fully connected competing Kuramoto model with a uniform intrinsic frequency distribution $g(\omega)$ was recently considered. This competing Kuramoto model assigns two coupling constants with opposite signs,…

Statistical Mechanics · Physics 2020-09-04 Jinha Park , B. Kahng

We consider a Kuramoto model of coupled oscillators that includes quenched random interactions of the type used by van Hemmen in his model of spin glasses. The phase diagram is obtained analytically for the case of zero noise and a…

Chaotic Dynamics · Physics 2015-06-17 Isabel M. Kloumann , Ian M. Lizarraga , Steven H. Strogatz

We study patterns observed right after the loss of stability of mixing in the Kuramoto model of coupled phase oscillators with random intrinsic frequencies on large graphs, which can also be random. We show that the emergent patterns are…

Chaotic Dynamics · Physics 2020-09-02 Hayato Chiba , Georgi S. Medvedev , Matthew S. Mizuhara

We consider the synchronization problem of swing equations, a second-order Kuramoto-type model, on connected networks with inhomogeneous dampings. This was largely motivated by its relevance to the dynamics of power grids. We focus on the…

Dynamical Systems · Mathematics 2016-10-27 Young-Pil Choi , Zhuchun Li

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

Statistical Mechanics · Physics 2007-05-23 M. Bahiana , M. S. O. Massunaga

We present an extension of the Kuramoto-Sakaguchi model for networks, deriving the second-order phase approximation for a paradigmatic model of oscillatory networks - an ensemble of non-identical Stuart-Landau oscillators coupled pairwisely…

Adaptation and Self-Organizing Systems · Physics 2024-08-14 Erik T. K. Mau , Oleh E. Omel'chenko , Michael Rosenblum