82 citations · 552 across the 32 of their papers we have counts for
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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…
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…
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…
Stability of twisted states in the Kuramoto model on Cayley and random graphs
Georgi S. Medvedev, Xuezhi Tang
The Kuramoto model (KM) of coupled phase oscillators on complete, Paley, and Erdos-Renyi (ER) graphs is analyzed in this work. As quasirandom graphs, the complete, Paley, and ER gr…
The geometry of spontaneous spiking in neuronal networks
Georgi S. Medvedev, Svitlana Zhuravytska
The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell larg…