82 citations · 552 across the 32 of their papers we have counts for
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Chimeras unfolded
Georgi S. Medvedev, Matthew S. Mizuhara
The instability of mixing in the Kuramoto model of coupled phase oscillators is the key to understanding a range of spatiotemporal patterns, which feature prominently in collective…
Instability of mixing in the Kuramoto model: From bifurcations to patterns
Hayato Chiba, Georgi S. Medvedev, Matthew S. Mizuhara
We study patterns observed right after the loss of stability of mixing in the Kuramoto model of coupled phase oscillators with random intrinsic frequencies on large graphs, which c…
Synchronization of coupled chaotic maps
Georgi S. Medvedev, Xuezhi Tang
We prove a sufficient condition for synchronization for coupled one-dimensional maps and estimate the size of the window of parameters where synchronization takes place. It is show…
Chaos at the border of criticality
Georgi S. Medvedev, Yun Yoo
The present paper points out to a novel scenario for formation of chaotic attractors in a class of models of excitable cell membranes near an Andronov-Hopf bifurcation (AHB). The m…
On transition to bursting via deterministic chaos
Georgi S. Medvedev
We study statistical properties of the irregular bursting arising in a class of neuronal models close to the transition from spiking to bursting. Prior to the transition to burstin…