Related papers: The Kuramoto Model with Time-Varying Parameters
The entrainment transition of coupled random frequency oscillators is revisited. The Kuramoto model (global coupling) is shown to exhibit unusual sample-dependent finite size effects leading to a correlation size exponent $\bar\nu=5/2$.…
The linear response is studied in globally coupled oscillator systems including the Kuramoto model. We develop a linear response theory which can be applied to systems whose coupling functions are generic. Based on the theory, we examine…
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…
Ecological systems, as is often noted, are complex. Equally notable is the generalization that complex systems tend to be oscillatory, whether Huygens simple patterns of pendulum entrainment or the twisted chaotic orbits of Lorenz…
This work considers an extension of the Kuramoto model with run-and-tumble dynamics -- a type of self-propelled motion. The difference between the extended and the original model is that in the extended version angular velocity of…
By means of numerical integration we investigate the coherent and incoherent phases in a generalized Kuramoto model of phase-coupled oscillators with distance-dependent delay. Preserving the topology of a complete graph, we arrange the…
We explore large populations of phase oscillators interacting via random coupling functions. Two types of coupling terms, the Kuramoto-Daido coupling and the Winfree coupling, are considered. Under the assumption of statistical independence…
We study the Kuramoto model for coupled oscillators. For the case of identical natural frequencies, we give a new proof of the complete frequency synchronization for all initial data; extending this result to the continuous version of the…
Understanding the sensitivity of a system's behavior with respect to parameter changes is essential for many applications. This sensitivity may be desired - for instance in the brain, where a large repertoire of different dynamics,…
Inspired by the Deffuant and Hegselmann-Krause models of opinion dynamics, we extend the Kuramoto model to account for confidence bounds, i.e., vanishing interactions between pairs of oscillators when their phases differ by more than a…
In order to discover generic effects of heterogeneous communication delays on the dynamics of large systems of coupled oscillators, this paper studies a modification of the Kuramoto model incorporating a distribution of interaction delays.…
Synchronization in a population of oscillators with hyperbolic chaotic phases is studied for two models. One is based on the Kuramoto dynamics of the phase oscillators and on the Bernoulli map applied to these phases. This system possesses…
We present an improved and more accurate numerical scheme for a generalization of the Kuramoto model of coupled phase oscillators to the three-dimensional space. The present numerical scheme relies crucially on our observation that the…
We investigate the diffusion coefficient of the time integral of the Kuramoto order parameter in globally coupled nonidentical phase oscillators. This coefficient represents the deviation of the time integral of the order parameter from its…
In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others…
Using recent dimensionality reduction techniques in large systems of coupled phase oscillators exhibiting bistability, we analyze complex macroscopic behavior arising when the coupling between oscillators is allowed to evolve slowly as a…
The Kuramoto model was recently extended to arbitrary dimensions by reinterpreting the oscillators as particles moving on the surface of unit spheres in a D-dimensional space. Each particle is then represented by a D-dimensional unit…
We consider the (noisy) Kuramoto model, that is a population of N oscillators, or rotators, with mean-field interaction. Each oscillator has its own randomly chosen natural frequency (quenched disorder) and it is stirred by Brownian motion.…
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 has provided deep insights into synchronization phenomena and remains an important paradigm to study the dynamics of coupled oscillators. Yet, despite its success, the asynchronous regime in the Kuramoto model has…