相关论文: Hyperbolic Geometry of Kuramoto Oscillator Network…
Stable subgroups and the Morse boundary are two systematic approaches to collect and study the hyperbolic aspects of finitely generated groups. In this paper we unify and generalize these strategies by viewing any geodesic metric space as a…
Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models,…
Globally coupled phase oscillator models, such as the Kuramoto model, exhibit spontaneous collective synchronization. Such models can be restated in terms of interactions within and between subsets of oscillators. An approximation for the…
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…
Collective oscillations and patterns of synchrony have long fascinated researchers in the applied sciences, particularly due to their far-reaching importance in chemistry, physics, and biology. The Kuramoto model has emerged as a…
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…
The Kuramoto model is a commonly used mathematical model for studying synchronized oscillations in biological systems, with its temporal synchronization properties well studied. However, the properties of spatial waves have received less…
The Kuramoto model is a classical nonlinear ODE system designed to study synchronization phenomena. Each equation represents the phase of an oscillator and the coupling between them is determined by a graph. There is an increasing interest…
We present a collective coordinate approach to describe coupled phase oscillators. We apply the method to study synchronisation in a Kuramoto model. In our approach an N-dimensional Kuramoto model is reduced to an n-dimensional ordinary…
The Kuramoto model, describing the synchronization dynamics of coupled oscillators, has been generalized in many ways over the past years. One recent extension of the model replaces the oscillators, originally characterized by a single…
We use the Gelfand-Tsetlin pattern to construct an effective Hamiltonian, completely integrable action of a torus T on an open dense subset of a coadjoint orbit of the unitary group. We then identify a proper Hamiltonian T-manifold centered…
This paper unifies the recent results on generalized Kuramoto Model reductions. Lohe took a coupled system of $N$ bodies on $S^d$ governed by the Kuramoto equations $\dot{x_i} = \Omega x_i + X - \langle x_i, X \rangle x_i$ and used the…
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…
We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space which evolve by an arbitrary (non-homogeneous) function of the radii of curvature. The associated flow of the radii of…
Compact hyperbolic 3-manifolds are used in cosmological models. Their topology is characterized by their homotopy group $\pi_1(M)$ whose elements multiply by path concatenation. The universal covering of the compact manifold $M$ is the…
We study the dynamics of the Kuramoto model on the sphere under higher-order interactions and an external periodic force. For identical oscillators, we introduce a novel way to incorporate three- and four-body interactions into the dynamics…
Higher order interactions can lead to new equilibrium states and bifurcations in systems of coupled oscillators described by the Kuramoto model. However, even in the simplest case of 3-body interactions there are more than one possible…
We consider a class of inhomogeneous self-similar cosmological models in which the perfect fluid flow is tangential to the orbits of a three-parameter similarity group. We restrict the similarity group to possess both an Abelian $G_{2}$,…
Electronic nematic order has been reported in a rich landscape of materials, encompassing not only a range of intertwined correlated and topological phenomena, but also different underlying lattice symmetries. Motivated by these findings,…
Motivated by the nematic electronic fluid phase in Sr_{3}Ru_{2}O_{7}, we develop a combined scheme of the renormalization-group method and the random-phase-approximation-type method, and analyze orbital susceptibilities of the…