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Related papers: Synchronization on star graph with noise

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In this paper, we study the phase transition behavior emerging from the interactions among multiple agents in the presence of noise. We propose a simple discrete-time model in which a group of non-mobile agents form either a fixed connected…

Optimization and Control · Mathematics 2008-10-21 Jialing Liu , Vikas Yadav , Hullas Sehgal , Joshua M. Olson , Haifeng Liu , Nicola Elia

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

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

We obtain exact results on autocorrelation of the order parameter in the nonequilibrium stationary state of a paradigmatic model of spontaneous collective synchronization, the Kuramoto model of coupled oscillators, evolving in presence of…

Statistical Mechanics · Physics 2018-10-10 Debraj Das , Shamik Gupta

We consider the celebrated Kuramoto model with nearest neighbour interactions, arranged on a two-dimensional square lattice in presence of two kinds of noise - annealed and quenched. We focus on both the steady state and relaxation dynamics…

Adaptation and Self-Organizing Systems · Physics 2020-04-02 Mrinal Sarkar

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 describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder - diversity of intrinsic oscillatory frequencies and external independent noise.…

Adaptation and Self-Organizing Systems · Physics 2015-06-23 Vladimir Vlasov , Maxim Komarov , Arkady Pikovsky

We consider a system of globally-coupled phase-only oscillators with distributed intrinsic frequencies and evolving in presence of distributed Gaussian, white noise, namely, a Gaussian, white noise whose strength for every oscillator is a…

Statistical Mechanics · Physics 2023-12-20 Alessandro Campa , Shamik Gupta

We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective…

Statistical Mechanics · Physics 2009-10-31 H. Hong , M. Y. Choi , K. Park , B. -G. Yoon , K. -S. Soh

Many natural and social phenomena are characterized by synchronization. The Kuramoto model, taking into account the basic ingredients for observing synchronized states, allows to study mathematically synchronization in a simplified but…

Statistical Mechanics · Physics 2019-10-08 Claudio Maggi , Matteo Paoluzzi

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

Synchronization in various complex networks is significantly influenced by higher-order interactions combined with non-Gaussian stochastic perturbations, yet their mechanisms remain mainly unclear. In this paper, we systematically…

Statistical Mechanics · Physics 2025-09-30 Dan Zhao , Jürgen Kurths , Norbert Marwan , Yong Xu

We study synchronization phenomenon in a self-correcting population of noisy phase oscillators with randomly distributed natural frequencies. In our model each oscillator stochastically switches its phase to the ensemble-averaged value…

Adaptation and Self-Organizing Systems · Physics 2016-03-17 Sergey Belan

We study the homogeneous Kuramoto model on a graph and the geometry of its underlying optimization landscape $\min_{\boldsymbol \theta \in \mathbb R^n}-\sum_{1\leq i,j\leq n} A_{ij}\cos(\theta_i-\theta_j).$ This problem admits a dual…

Combinatorics · Mathematics 2026-05-05 Hongjin Wu , Ulrik Brandes

In his classical work, Kuramoto analytically described the onset of synchronization in all-to-all coupled networks of phase oscillators with random intrinsic frequencies. Specifically, he identified a critical value of the coupling…

Dynamical Systems · Mathematics 2018-08-15 Hayato Chiba , Georgi S. Medvedev , Matthew S. Mizuhara

Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to…

Optimization and Control · Mathematics 2011-06-28 Florian Dorfler , Francesco Bullo

A knot is a circle embedded in the space. Projecting a knot on a plane, we obtain a diagram which is known as the knot diagram. The vertices of the diagram, where the curved lines are crossed, can be considered as sites occupied by…

Computational Physics · Physics 2015-11-26 Amelia Carolina Sparavigna

We study the emergence of synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and a time delay is…

Statistical Mechanics · Physics 2012-03-07 Thomas Kauê Dal'Maso Peron , Francisco Aparecido Rodrigues

The Kuramoto model can be formulated as a gradient flow on a nonconvex energy landscape of the form $E(\boldsymbol{\theta}) := \frac{1}{2} \sum_{1\le i,j\le n} A_{ij}\bigl(1-\cos(\theta_i-\theta_j)\bigr).$ A fundamental question is to…

Dynamical Systems · Mathematics 2026-02-06 Hongjin Wu , Ulrik Brandes

Can synchronization properties of a network of identical oscillators in the presence of noise be improved through appropriate rewiring of its connections? What are the optimal network architectures for a given total number of connections?…

Adaptation and Self-Organizing Systems · Physics 2013-05-30 Tatsuo Yanagita , Alexander S. Mikhailov