82 citations · 552 across the 32 of their papers we have counts for
9 papers · 1 filter
Stability and bifurcation of mixing in the Kuramoto model with inertia
Hayato Chiba, Georgi S. Medvedev
The Kuramoto model of coupled second order damped oscillators on convergent sequences of graphs is analyzed in this work. The oscillators in this model have random intrinsic freque…
Bifurcations in the Kuramoto model on graphs
Hayato Chiba, Georgi S. Medvedev, Matthew S. Mizuhara
In his classical work, Kuramoto analytically described the onset of synchronization in all-to-all coupled networks of phase oscillators with random intrinsic frequencies. Specifica…
The continuum limit of the Kuramoto model on sparse random graphs
Georgi S. Medvedev
In this paper, we study convergence of coupled dynamical systems on convergent sequences of graphs to a continuum limit. We show that the solutions of the initial value problem for…
The mean field analysis of the Kuramoto model on graphs II. Asymptotic stability of the incoherent state, center manifold reduction, and bifurcations
Hayato Chiba, Georgi S. Medvedev
In our previous work [Chiba, Medvedev, arXiv:1612.06493], we initiated a mathematical investigation of the onset of synchronization in the Kuramoto model (KM) of coupled phase osci…
The mean field equation for the Kuramoto model on graph sequences with non-Lipschitz limit
Dmitry Kaliuzhnyi-Verbovetskyi, Georgi S. Medvedev
The Kuramoto model (KM) of coupled phase oscillators on graphs provides the most influential framework for studying collective dynamics and synchronization. It exhibits a rich repe…
The mean field analysis for the Kuramoto model on graphs I. The mean field equation and transition point formulas
Hayato Chiba, Georgi S. Medvedev
In his classical work on synchronization, Kuramoto derived the formula for the critical value of the coupling strength corresponding to the transition to synchrony in large ensembl…