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Emergence of generalized synchronization patterns in a ring of identical and locally coupled Kuramoto-type rotators are investigated by different methods. These approaches offer a useful visual picture for understanding the complexity of…

Pattern Formation and Solitons · Physics 2019-07-24 Károly Dénes , Bulcsú Sándor , Zoltán Néda

We consider a toy model of two kinetically coupled stochastic oscillators whose dynamics is described as a Markov jump process among $N$ discrete phase states. For large $N$, it maps onto the deterministic two-oscillator Kuramoto model of…

Statistical Mechanics · Physics 2026-03-24 Maciej Chudak , Massimiliano Esposito , Krzysztof Ptaszynski

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

In this paper, we investigate synchronization of coupled second-order linear harmonic oscillators with random noises and time delays. The interaction topology is modeled by a weighted directed graph and the weights are perturbed by white…

Data Analysis, Statistics and Probability · Physics 2009-09-29 Yilun Shang

The synchronization phenomenon is ubiquitous in nature. In ensembles of coupled oscillators, explosive synchronization is a particular type of transition to phase synchrony that is first-order as the coupling strength increases. Explosive…

Adaptation and Self-Organizing Systems · Physics 2020-01-23 Inmaculada Leyva , Cristina Masoller

Imagine a group of oscillators, each endowed with their own rhythm or frequency, be it the ticking of a biological clock, the swing of a pendulum, or the glowing of fireflies. While these individual oscillators may seem independent of one…

Dynamical Systems · Mathematics 2025-01-13 Abhiram Gorle

We study the emergence of synchronization in the Kuramoto model on a digraph in the presence of time delays. Assuming the digraph is strongly connected, we first establish a uniform bound on the phase diameter and subsequently prove the…

Optimization and Control · Mathematics 2024-06-05 Conor Carty , Young-Pil Choi , Chiara Cicolani , Cristina Pignotti

Kuramoto model is one of the most prominent models for the synchronization of coupled oscillators. It has long been a research hotspot to understand how natural frequencies, the interaction between oscillators, and network topology…

Adaptation and Self-Organizing Systems · Physics 2020-04-08 Shuyang Ling

Improving the frequency precision by synchronizing a lattice of oscillators is studied in the phase reduction limit. For the most commonly studied case of purely dissipative phase coupling (the Kuramoto model) I confirm that the frequency…

Pattern Formation and Solitons · Physics 2013-05-30 M. C. Cross

We explore identical R\"ossler systems organized into two equally-sized groups, among which differing positive and negative in- and out-coupling strengths are allowed. Patterns of distinctly synchronized phase dynamics are observed, which…

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

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

Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rhythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards…

Statistical Mechanics · Physics 2014-11-11 Ignacio Hermoso de Mendoza , Leonardo A. Pachón , Jesús Gómez-Gardeñes , David Zueco

Synchronization in networks of coupled oscillators is a widely studied topic with extensive scientific and engineering applications. In this paper, we study the frequency synchronization problem for networks of Kuramoto oscillators with…

Optimization and Control · Mathematics 2018-09-25 Saber Jafarpour , Elizabeth Y. Huang , Francesco Bullo

We generalize the Kuramoto model for the synchronization transition of globally coupled phase oscillators to populations by incorporating an additional heterogeneity with the coupling strength, where each oscillator pair interacts with…

Adaptation and Self-Organizing Systems · Physics 2016-12-21 Can Xu , Jian Gao , Hairong Xiang , Wenjing Jia , Shuguang Guan , Zhigang Zheng

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

We consider a system of N phase oscillators having randomly distributed natural frequencies and diagonalizable interactions among the oscillators. We show that in the limit of N going to infinity, all solutions of such a system are…

Dynamical Systems · Mathematics 2007-05-23 Takashi Nishikawa , Frank C. Hoppensteadt

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

The transition to synchrony in the Kuramoto model of globally coupled phase oscillators with a uniform distribution of natural frequencies is discontinuous. We extend the theory of this transition to the Kuramoto-Sakaguchi model, taking…

Adaptation and Self-Organizing Systems · Physics 2026-04-14 Arkady Pikovsky

Synchronization in quantum systems has been recently studied through persistent oscillations of local observables, which stem from undamped modes of the dissipative dynamics. However, the existence of such modes requires fine-tuning the…

Quantum Physics · Physics 2025-10-14 Yi J. Zhao , Joel E. Moore , Juzar Thingna , Christopher W. Wächtler