Related papers: Kuramoto model with frequency-degree correlations …
We consider the synchronization of oscillators in complex networks where there is an interplay between the oscillator dynamics and the network topology. Through a remarkable transformation in parameter space and the introduction of virtual…
We study the emergence of synchronization in scale-free networks by considering the Kuramoto model of coupled phase oscillators. The natural frequencies of oscillators are assumed to be correlated with their degrees and a time delay is…
By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…
We study the impact of network heterogeneity on relaxation dynamics of the Kuramoto model on uncorrelated complex networks with scale-free degree distributions. Using the Ott-Antonsen method and the annealed-network approach, we find that…
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…
We study the impact of random pinning fields on the emergence of synchrony in the Kuramoto model on complete graphs and uncorrelated random complex networks. We consider random fields with uniformly distributed directions and homogeneous…
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 consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we…
The Kuramoto model is a classical mathematical model in the field of non-linear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network's…
The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies. The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling…
Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal…
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent…
Kuramoto oscillators have been proposed earlier as a model for interacting systems that exhibit synchronisation. In this article we study the difference between networks with symmetric and asymmetric distribution of natural frequencies. We…
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…
The Kuramoto model of a network of coupled phase oscillators exhibits a first-order phase transition when the distribution of natural frequencies has a finite flat region at its maximum. First-order phase transitions including hysteresis…
Explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. In the current work, we took into account mean-field approximations to determine the…
We investigate the synchronization transition of the modified Kuramoto model where the oscillators form a scale-free network with degree exponent $\lambda$. An oscillator of degree $k_i$ is coupled to its neighboring oscillators with…
A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of limit-cycle oscillators of distributed frequencies that are globally coupled…
We consider a mean-field model of coupled phase oscillators with quenched disorder in the natural frequencies and coupling strengths. A fraction $p$ of oscillators are positively coupled, attracting all others, while the remaining fraction…
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…