82 citations · 552 across the 32 of their papers we have counts for
Showing 2016Show all
3 papers · 1 filter
math.DS2016★ 4 cited
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…
nlin.PS2016★ 23 cited
Stability of twisted states in the continuum Kuramoto model
Georgi S. Medvedev, J. Douglas Wright
We study a nonlocal diffusion equation approximating the dynamics of coupled phase oscillators on large graphs. Under appropriate assumptions, the model has a family of steady stat…
math.DS2016★ 38 cited
The semilinear heat equation on sparse random graphs
Dmitry Kaliuzhnyi-Verbovetskyi, Georgi S. Medvedev
Using the theory of -graphons (Borgs et al, 2014), we derive and rigorously justify the continuum limit for systems of differential equations on sparse random graphs. Specific…