82 citations · 552 across the 32 of their papers we have counts for
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nlin.AO2013★ 61 cited
Small-world networks of Kuramoto oscillators
Georgi S. Medvedev
The Kuramoto model of coupled phase oscillators on small-world (SW) graphs is analyzed in this work. When the number of oscillators in the network goes to infinity, the model acqui…
nlin.AO2013★ 82 cited
The nonlinear heat equation on W-random graphs
Georgi S. Medvedev
For systems of coupled differential equations on a sequence of W-random graphs, we derive the continuum limit in the form of an evolution integral equation. We prove that solutions…
nlin.AO2013
The nonlinear heat equation on dense graphs and graph limits
Georgi S. Medvedev
We use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking continuum…