82 citations · 552 across the 32 of their papers we have counts for
34 papers
Turing bifurcation in the Swift-Hohenberg equation on deterministic and random graphs
Georgi S. Medvedev, Dmitry E. Pelinovsky
The Swift-Hohenberg equation (SHE) is a partial differential equation that explains how patterns emerge from a spatially homogeneous state. It has been widely used in the theory of…
Galerkin method for nonlocal diffusion equations on self-similar domains
Georgi S. Medvedev
Integro-differential equations, analyzed in this work, comprise an important class of models of continuum media with nonlocal interactions. Examples include peridynamics, populatio…
Bifurcations and patterns in the Kuramoto model with inertia
Hayato Chiba, Georgi S. Medvedev, Matthew S. Mizuhara
In this work, we analyze the Kuramoto model (KM) with inertia on a convergent family of graphs. It is assumed that the intrinsic frequencies of the individual oscillators are sampl…
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…
A Numerical Method for a Nonlocal Diffusion Equation with Additive Noise
Georgi Medvedev, Gideon Simpson
We consider a nonlocal evolution equation representing the continuum limit of a large ensemble of interacting particles on graphs forced by noise. The two principle ingredients of…
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…