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Synchronization in networks of coupled oscillators is known to be largely determined by the spectral and symmetry properties of the interaction network. Here we leverage this relation to study a class of networks for which the threshold…

Adaptation and Self-Organizing Systems · Physics 2017-12-21 Takashi Nishikawa , Adilson E. Motter

In this paper, we consider an $N$-oscillators complexified Kuramoto model. We first observe that there are solutions exhibiting finite-time blow-up behavior in all coupling regimes. When the coupling strength $\lambda>\lambda_c$, sufficient…

Dynamical Systems · Mathematics 2026-01-21 Ting-Yang Hsiao , Yun-Feng Lo , Winnie Wang

The present paper introduces a linear reformulation of the Kuramoto model describing a self-synchronizing phase transition in a system of globally coupled oscillators that in general have different characteristic frequencies. The…

Pattern Formation and Solitons · Physics 2008-03-18 David C. Roberts

Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization…

Statistical Mechanics · Physics 2019-10-16 Thomas Peron , Bruno Messias , Angélica S. Mata , Francisco A. Rodrigues , Yamir Moreno

For the Kuramoto model and its variations, it is difficult to analyze the exponential synchronization under the general digraphs due to the lack of symmetry. %due to the asymmetry of the adjacency matrices. In this paper, for the…

Optimization and Control · Mathematics 2018-08-23 Jinxing Zhang , Jiandong Zhu

We present a formula for determining synchronizability in large, randomized and weighted simplicial complexes. This formula leverages eigenratios and costs to assess complete synchronizability under diverse network topologies and intensity…

Adaptation and Self-Organizing Systems · Physics 2024-05-03 S. Nirmala Jenifer , Dibakar Ghosh , Paulsamy Muruganandam

The conditions under which synchronization is achieved for a one-dimensional ring of identical phase oscillators with Kuramoto-like local coupling are studied. The system is approached in the weakly coupled approximation as phase units.…

Adaptation and Self-Organizing Systems · Physics 2023-10-20 K. García Medina , E. Estevez-Rams

We study the synchronization of a small-world network of identical coupled phase oscillators with Kuramoto interaction. First, we consider the model with instantaneous mutual interaction and the normalized coupling constant to the degree of…

Disordered Systems and Neural Networks · Physics 2017-05-23 Sara Ameli , Farhad Shahbazi , Maryam Karimian , Tahereh Malakoutikhah

The synchronization behavior of networked chaotic oscillators with periodic coupling is investigated. It is observed in simulations that the network synchronizability could be significantly influenced by tuning the coupling frequency, even…

Chaotic Dynamics · Physics 2018-07-18 Sansan Li , Na Sun , Li Chen , Xingang Wang

Populations of flashing fireflies, claps of applauding audience, cells of cardiac and circadian pacemakers reach synchrony via event-triggered interactions, referred to as pulse couplings. Synchronization via pulse coupling is widely used…

Systems and Control · Computer Science 2017-10-16 Anton V. Proskurnikov , Ming Cao

In our previous work [Chiba, Medvedev, arXiv:1612.06493], we initiated a mathematical investigation of the onset of synchronization in the Kuramoto model (KM) of coupled phase oscillators on convergent graph sequences. There, we derived and…

Dynamical Systems · Mathematics 2018-04-24 Hayato Chiba , Georgi S. Medvedev

Multi-qubit quantum processors coupled to networking provides the state-of-the-art quantum computing platform. However, each qubit has unique eigenfrequency even though fabricated in the same process. To continue quantum gate operations…

Quantum Physics · Physics 2023-01-12 Abhijit Bhattacharyya

This paper studies stability properties of multi-cluster formations in Kuramoto networks with adaptive coupling. Sufficient conditions for the local asymptotic stability of the corresponding synchronization invariant toroidal manifold are…

Systems and Control · Electrical Eng. & Systems 2021-04-16 Petro Feketa , Alexander Schaum , Thomas Meurer

Synchronization is an ubiquitous phenomenon in dynamical systems of networked oscillators. While it is often a goal to achieve, in some context one would like to decrease it, e.g., although synchronization is essential to the good…

Dynamical Systems · Mathematics 2025-04-07 Martin Moriamé , Timoteo Carletti

We generalize the Kuramoto model of globally coupled oscillators to multifrequency communities. A situation when mean frequencies of two subpopulations are close to resonance 2:1 is considered in detail. We derive uniformly rotating…

Adaptation and Self-Organizing Systems · Physics 2015-02-24 Maxim Komarov , Arkady Pikovsky

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

Determining the number of stable phase-locked solutions for locally coupled Kuramoto models is a long-standing mathematical problem with important implications in biology, condensed matter physics and electrical engineering among others. We…

Adaptation and Self-Organizing Systems · Physics 2016-04-05 Robin Delabays , Tommaso Coletta , Philippe Jacquod

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 case study of how topology can affect synchronization. Specifically, we consider arrays of phase oscillators coupled in a ring or a chain topology. Each ring is perfectly matched to a chain with the same initial conditions and…

Dynamical Systems · Mathematics 2016-12-07 Bertrand Ottino-Loffler , Steven Strogatz

We present a rigorous mathematical framework establishing the equivalence of four classical notions of synchronization full phase-locking, phase-locking, frequency synchronization, and order parameter synchronization in generalized Kuramoto…

Dynamical Systems · Mathematics 2026-05-29 Ting-Yang Hsiao , Yun-Feng Lo , Chengbin Zhu