Related papers: Exponential dephasing of oscillators in the Kineti…
We study the kinetic Kuramoto model for coupled oscillators. We prove that for any regular asymptotically free state, if the interaction is small enough, it exists a solution which is asymptotically close to it. For this class of solution…
We consider the Kuramoto model of globally coupled phase oscillators in its continuum limit, with individual frequencies drawn from a distribution with density of class $C^n$ ($n\geq 4$). A criterion for linear stability of the uniform…
We study Kuramoto phase oscillators with temporal fluctuations in the frequencies. The infinite-dimensional system can be reduced in a Gaussian approximation to two first-order differential equations. This yields a solution for the…
The Kuramoto model, which serves as a paradigm for investigating synchronization phenomenon of oscillatory system, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here, we generalize…
Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all…
Frustrated random interactions are a key ingredient of spin glasses. From this perspective, we study the dynamics of the Kuramoto model with quenched random couplings: the simplest oscillator ensemble with fully disordered interactions. We…
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…
The Kuramoto model with high-order coupling has recently attracted some attention in the field of coupled oscillators in order, for instance, to describe clustering phenomena in sets of coupled agents. Instead of considering interactions…
We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent…
The Kuramoto model serves as a paradigm to study the phenomenon of spontaneous collective synchronization. We study here a nontrivial generalization of the Kuramoto model by including an interaction that breaks explicitly the rotational…
We present an approach for the description of fluctuations that are due to finite system size induced correlations in the Kuramoto model of coupled oscillators. We construct a hierarchy for the moments of the density of oscillators that is…
We study populations of oscillators, all-to-all coupled by means of quenched disordered phase shifts. While there is no traditional synchronization transition with a nonvanishing Kuramoto order parameter, the system demonstrates a specific…
The dynamics of dissipative topological defects in a system of coupled phase oscillators, arranged in one and two-dimensional arrays, is numerically investigated using the Kuramoto model. After an initial rapid decay of the number of…
The dynamics of large systems of coupled oscillators is a subject of increasing importance with prominent applications in several areas such as physics and biology. The Kuramoto model, where a set of oscillators move around a circle…
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 present an equation-free multi-scale approach to the computational study of the collective dynamics of the Kuramoto model [{\it Chemical Oscillations, Waves, and Turbulence}, Springer-Verlag (1984)], a prototype model for coupled…
We investigate the scaling properties of the order parameter and the largest nonvanishing Lyapunov exponent for the fully locked state in the Kuramoto model with a finite number $N$ of oscillators. We show that, for any finite value of $N$,…
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…
The Kuramoto model provides a concrete mathematical realization of emergent synchrony in a population of phase-coupled oscillators. Since Kuramoto's publication, \textit{Oscillations, Waves, and Turbulence}, researchers have worked to…
The emergence of collective synchrony from an incoherent state is a phenomenon essentially described by the Kuramoto model. This canonical model was derived perturbatively, by applying phase reduction to an ensemble of heterogeneous,…