相关论文: Synchronization and multi-cluster capabilities of …
When the natural frequencies are allocated symmetrically in the Kuramoto model there exists an invariant torus of dimension [N/2]+1 (N is the population size). A global phase shift invariance allows to reduce the model to $N-1$ dimensions…
In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of the coupling strength between two oscillators is governed by the…
We consider networks of coupled phase oscillators of different complexity: Kuramoto-Daido-type networks, generalized Winfree networks, and hypernetworks with triple interactions. For these setups an inverse problem of reconstruction of the…
There are a number of models of coupled oscillator networks where the question of the stability of fixed points reduces to calculating the index of a graph Laplacian. Some examples of such models include the Kuramoto and Kuramoto--Sakaguchi…
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the…
After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: deterministic coupling and common forcing. The inclusion of independent random forcing in these models typically…
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…
The Kuramoto model constitutes a paradigmatic model for the dissipative collective dynamics of coupled oscillators, characterizing in particular the emergence of synchrony. Here we present a classical Hamiltonian (and thus conservative)…
We investigate the stability of the synchronization manifold in a ring and an open-ended chain of nearest neighbors coupled self-sustained systems, each self-sustained system consisting of multi-limit cycles van der Pol oscillators. Such…
We present and analyze a nonabelian version of the Kuramoto system, which we call the quantum Kuramoto system. We study the stability of several classes of special solutions to this system, and show that for certain connection topologies…
Based on a local greedy numerical algorithm, we compute the topology of weighted, directed, and of unlimited extension networks of non identical Kuramoto oscillators which simultaneously satisfy 2 criteria: i) global frequency…
Motivated by the recent and growing interest in smart grid technology, we study the operation of DC/AC inverters in an inductive microgrid. We show that a network of loads and DC/AC inverters equipped with power-frequency droop controllers…
We investigate the dynamics of a two-dimensional array of oscillators with phase-shifted coupling. Each oscillator is allowed to interact with its neighbors within a finite radius. The system exhibits various patterns including squarelike…
The mean field Kuramoto model describing the synchronization of a population of phase oscillators with a bimodal frequency distribution is analyzed (by the method of multiple scales) near regions in its phase diagram corresponding to…
Synchronization is observed in many natural systems, with examples ranging from neuronal activation to walking pedestrians. The models proposed by Winfree and Kuramoto stand as the classic frameworks for investigating these phenomena. The…
Can a simple oscillator system, as in cellular automata, sustain complex nature upon discretization in time and space? The answer is by no means trivial as even the most simple, two-state, nearest neighbours cellular automata can lead to…
We consider the Kuramoto model of coupled oscillators, specifically the case of tree networks, for which we prove a simple closed-form expression for the critical coupling. For several classes of tree, and for both uniform and Gaussian…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
We provide conditions on the coupling function such that a system of 4 globally coupled identical oscillators has chaotic attractors, a pair of Lorenz attractors or a 4-winged analogue of the Lorenz attractor. The attractors emerge near the…
We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to a number of states unsupported by…