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We propose a Kuramoto model of coupled oscillators on a time-varying graph, whose dynamics is dictated by a Markov process in the space of graphs. The simplest representative is considering a base graph and then the subgraph determined by…
We study the synchronized behavior of the inertial Kuramoto oscillators with frustration effect under a symmetric and connected network. Due to the lack of second-order gradient flow structure and singularity of second-order derivative of…
We study synchronization properties of coupled oscillators on networks that allow description in terms of global mean field coupling. These models generalize the standard Kuramoto-Sakaguchi model, allowing for different contributions of…
We study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the non-vanishing order parameter). The newly developed…
Despite their simplicity, networks of coupled phase oscillators can give rise to intriguing collective dynamical phenomena. However, the symmetries of globally and identically coupled identical units do not allow solutions where distinct…
The Kuramoto model is the simplest case of globally coupled phase oscillators with a purely sinusoidal fundamental-harmonic phase coupling function, whose dynamical properties have been extensively studied. While coupled phase oscillators…
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.…
Kuramoto model is one of the most prominent models for the synchronization of coupled oscillators. It has long been a research hotspot to understand how natural frequencies, the interaction between oscillators, and network topology…
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 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…
Previous results have shown that a large class of complex systems consisting of many interacting heterogeneous phase oscillators exhibit an attracting invariant manifold. This result has enabled reduced analytic system descriptions from…
In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we…
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…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
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…
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,…
Improving the frequency precision by synchronizing a lattice of oscillators is studied in the phase reduction limit. For the most commonly studied case of purely dissipative phase coupling (the Kuramoto model) I confirm that the frequency…
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…
Super-critical Kuramoto oscillators with distributed frequencies separate into two disjoint groups: an ordered one locked to the mean field, and a disordered one consisting of effectively decoupled oscillators -- at least so in the…
We propose a modification of the Kuramoto model to account for the effective change in the coupling constant among the oscillators, as suggested by some experiments on Josephson junction, laser arrays and mechanical systems, where the…