82 citations · 552 across the 32 of their papers we have counts for
9 papers · 1 filter
A global bifurcation organizing rhythmic activity in a coupled network
Georgi S. Medvedev, Matthew S. Mizuhara, Andrew Phillips
We study a system of coupled phase oscillators near a saddle-node on an invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control para…
Stability of clusters in the second-order Kuramoto model on random graphs
Georgi S. Medvedev, Matthew S. Mizuhara
The Kuramoto model of coupled phase oscillators with inertia on Erdos-Renyi graphs is analyzed in this work. For a system with intrinsic frequencies sampled from a bimodal distribu…
The Kuramoto model on power law graphs
Georgi S. Medvedev, Xuezhi Tang
The Kuramoto model (KM) of coupled phase oscillators on scale free graphs is analyzed in this work. The W-random graph model is used to define a convergent family of sparse graphs…
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…
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…
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…