相关论文: Mean field Kuramoto models on graphs
Recently, there has been considerable interest in the study of spontaneous synchronization, particularly within the framework of the Kuramoto model. The model comprises oscillators with distributed natural frequencies interacting through a…
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…
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…
We study the synchronisation properties of the Kuramoto model of coupled phase oscillators on a general network. Here we distinguish the ability of such a system to self-synchronise from the stability of this behaviour. While…
Employing the Kuramoto model as an illustrative example, we show how the use of the mean field approximation can be applied to large networks of phase oscillators with assortativity. We then use the ansatz of Ott and Antonsen [Chaos 19,…
The Kuramoto model has shaped our understanding of synchronization in complex systems, yet its phase-only formulation neglects amplitude dynamics that are intrinsic to many oscillatory networks. In this work, we revisit Kuramoto-type…
In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing a spanning tree. We provide a sufficient condition for the emergence of asymptotical synchronization if the initial data…
This paper presents new methods and results on almost global synchronization of coupled Hopf nonlinear oscillators, which are commonly used as the dynamic model of engineered central pattern generators (CPGs). On balanced graphs, any…
We consider the Kuramoto model on sparse random networks such as the Erd\H{o}s-R\'enyi graph or its combination with a regular two-dimensional lattice and study the dynamical scaling behavior of the model at the synchronization transition…
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…
Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously…
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…
The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N…
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…
This paper presents a distributed synchronization strategy for connected and automated vehicles in traffic networks. The strategy considers vehicles traveling from one intersection to the next as waves. The phase angle and frequency of each…
This paper studies a mean field game formulation of the classical Kuramoto model for synchronization. Our model captures the diversity within the population by considering random intrinsic frequencies, which allows us to study the impact of…
We investigate synchronization in the Kuramoto model with noise on a star graph. By revising the case of a complete graph, we propose a closed form of self-consistency equation for the conventional order parameter and generalize it for a…
Orientation-rich images, such as fingerprints and textures, often exhibit coherent angular directional patterns that are challenging to model using standard generative approaches based on isotropic Euclidean diffusion. Motivated by the role…
In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we…
A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of limit-cycle oscillators of distributed frequencies that are globally coupled…