Related papers: On the exponential synchronization for the asymmet…
The Kuramoto model with higher-order interactions has recently been shown to exhibit bistability, explosive synchronization transitions, and rich collective dynamics. Existing analytical approaches, however, typically rely on all-to-all…
When modeling the classical Kuramoto model, one of the key features is the tendency to synchronize. Accordingly, the most well-adopted choice of the coupling function is the sine function. Due to the oddness of the sine function, the…
One of a classical synchronization model is the Kuramoto model. We propose both first and second order Kuramoto dynamical models on graphs using discrete optimal transport dynamics. We analyze the synchronization behaviors for some examples…
We explore chaos in the Kuramoto model with multimodal distributions of the natural frequencies of oscillators and provide a comprehensive description under what conditions chaos occurs. For a natural frequency distribution with $M$ peaks…
This study investigates perturbation strategies inspired by adversarial attack principles from deep learning, designed to control synchronization dynamics through strategically crafted weak perturbations. We propose a gradient-based…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
Synchronization and desynchronization are the two ends on the spectrum of emergent phenomena that somehow often coexist in biological, neuronal, and physical networks. However, previous studies essentially regard their coexistence as a…
A class of adaptation functions is found for which a synchronous oscillation mode exists in the network of phase oscillators with triadic couplings. It is shown that the destruction of the synchronous mode occurs differently for networks…
We investigate the phenomenon of transition to synchronization in Sakaguchi-Kuramoto model in the presence of higher-order interactions and global order parameter adaptation. The investigation is done by performing extensive numerical…
Now a standard in Nonlinear Sciences, the Kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phenomenology has been sketched in early works, the…
We study the nonconvex optimization landscapes of synchronization problems on spheres. First, we present new results for the statistical problem of synchronization over the two-element group $\mathbf{Z}_2$. We consider the nonconvex…
We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an…
We investigate synchronization in the Kuramoto model with noise on a star graph. By revising the case of a complete graph, we propose a closed form of self-consistency equation for the conventional order parameter and generalize it for a…
We investigate synchronization in networks of Kuramoto oscillators with inertia. More specifically, we introduce a rewiring algorithm consisting basically in a {\em hill climb} scheme in which the edges of the network are swapped in order…
The Kuramoto model is a classical model used in the study of spontaneous synchronizations in networks of coupled oscillators. In this model, frequency synchronization configurations can be formulated as complex solutions to a system of…
We discuss in detail a human scale example of the synchronization phenomenon, namely the dynamics of the rhythmic applause. After a detailed experimental investigation, we describe the phenomenon with an approach based on the classical…
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…
Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global…
Although the mathematical study on the synchronization of wave equations at finite horizon has been well developed, there was few results on the synchronization of wave equations for long-time horizon. The aim of the paper is to investigate…
We propose the Kuramoto Graph Neural Network (KuramotoGNN), a novel class of continuous-depth graph neural networks (GNNs) that employs the Kuramoto model to mitigate the over-smoothing phenomenon, in which node features in GNNs become…