Related papers: Ott-Antonsen ansatz for the D-dimensional Kuramoto…
The celebrated Ott-Antonsen ansatz for coupled oscillators provides a useful framework to work with deterministic systems in the thermodynamic limit, but remains just an approximation for stochastic models. In this paper, I construct a…
The synchronization phenomena in thermoacoustic systems leading to oscillatory instability can effectively be modeled using Kuramoto oscillators. Such models consider the nonlinear response of flame as an ensemble of Kuramoto phase…
The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a {\it frustrated} version that…
We investigate the effect of partial order parameter adaptation in form of general functions on the synchronization behavior of coupled Kuramoto oscillators on top of random hypergraph models. The interactions between the oscillators are…
The second-order Kuramoto equation describes synchronization of coupled oscillators with inertia, which occur in power grids for example. Contrary to the first-order Kuramoto equation it's synchronization transition behavior is much less…
We propose a coupled system of fast and slow phase oscillators. We observe two-step transitions to quasi-periodic motions by direct numerical simulations of this coupled oscillator system. A low-dimensional equation for order parameters is…
Understanding the mechanisms that govern collective synchronization is a paramount task in nonlinear dynamics. While higher-order (many-body) interactions have recently emerged as a powerful framework for capturing collective behaviors,…
We introduce and investigate the effects of a new class of stochastic resetting protocol called subsystem resetting, whereby a subset of the system constituents in a many-body interacting system undergoes bare evolution interspersed with…
We consider an ensemble of phase oscillators in the thermodynamic limit, where it is described by a kinetic equation for the phase distribution density. We propose an ansatz for the circular moments of the distribution (Kuramoto-Daido order…
In the context of the Kuramoto model of coupled oscillators with distributed natural frequencies interacting through a time-delayed mean-field, we derive as a function of the delay exact results for the stability boundary between the…
We generalize the Kuramoto model by interpreting the $N$ variables on the unit circle as eigenvalues of a $N$-dimensional unitary matrix $U$, in three versions: general unitary, symmetric unitary and special orthogonal. The time evolution…
What happens when the paradigmatic Kuramoto model involving interacting oscillators of distributed natural frequencies and showing spontaneous collective synchronization in the stationary state is subject to random and repeated…
We uncover a solvable generalization of the Kuramoto model in which shears (or nonisochronicities) and natural frequencies are distributed and statistically dependent. We show that the strength and sign of this dependence greatly alter…
We analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed. The dynamics of this system has been the subject of long-standing interest. In 1984 Kuramoto proposed several conjectures…
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…
The Kuramoto model, despite its popularity as a mean-field theory for many synchronization phenomenon of oscillatory systems, is limited to a first-order harmonic coupling of phases. For higher-order coupling, there only exists a…
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 generalize the Kuramoto model for the synchronization transition of globally coupled phase oscillators to populations by incorporating an additional heterogeneity with the coupling strength, where each oscillator pair interacts with…
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…
The emergence of collective synchronization was reproduced long ago by Winfree in a classical model consisting of an ensemble of pulse-coupled phase oscillators. By means of the Ott-Antonsen ansatz, we derive an exact low-dimensional…