Georgi S. Medvedev
Georgi Medvedev
Professor



Department of Mathematics
Drexel University
3141 Chestnut Street
Philadelphia, PA 19104
phone: (215) 895-6612
fax: (215) 895-1582
email: medvedev@drexel.edu

Office: 292, Korman Center


Georgi Medvedev received Ph.D. in Mathematics from Boston University in 1999. Before coming to Drexel University in 2002, he was a Veblen Research Instructor at Princeton University and at the Institute for Advanced Study.

Dr. Medvedev teaches courses at all levels. He developed an interdisciplinary graduate course MATH 723 Mathematical Neuroscience.

He serves on the editorial board of Discrete and Continous Dynamical Systems (Series B) .


Teaching (past classes)

MATH 291: Complex and Vector Analysis for Engineers

MATH 510: Advanced Probability and Statistics I


Research

Dr. Medvedev's research interests include dynamical systems, network science, and mathematical biology. He is interested in combinatorial and stochastic aspects of network dynamics and synchronization; effects of noise on dynamics of nonlinear systems; and applications to neuroscience.

Dr. Medvedev's research on dynamical networks has been supported by National Science Foundation through grants

  • #1715161    Mean Field Analysis of Dynamical Networks,   2017-20,
  • #1412066    Dynamics of Large Networks,                             2014-17,
  • #1109367    Mathematical Analysis of Synchronization,        2011-14.


Recent publications (full list by area or chronologically )

* D. Kaliuzhnyi-Verbovetskyi and G.S. Medvedev, The mean field equation for the Kuramoto model on graph sequences with non-Lipschitz limit, submitted.   arxiv

* G.S. Medvedev and X. Tang, The Kuramoto model on power law graphs, submitted.   arxiv

* H. Chiba and G.S. Medvedev, The mean field analysis of the Kuramoto model on graphs I. The mean field equation and transition point formulas, submitted.   arxiv

* D. Kaliuzhnyi-Verbovetskyi and G.S. Medvedev, The semilinear heat equation on sparse random graphs, SIAM J. Math. Anal., 49(2), 1333-1355, 2017.   abstract   pdf

* G.S. Medvedev and J.D. Wright, Stability of twisted states in the continuum Kuramto model, SIAM J. Appl. Dyn. Syst., 16(1), 188-203, 2017.   abstract   pdf

* P. Hitczenko and G.S. Medvedev, Stability of equilibria of randomly perturbed maps, Discrete and Continuous Dynamical Systems - B, 22(2), 2017.   abstract   pdf

* G.S. Medvedev and X. Tang, Synchronization of coupled chaotic maps, Physica D304-305, pp. 42-51,2015.   abstract

* G.S. Medvedev and X. Tang, Stability of twisted states in the Kuramoto model on Cayley and random graphs, Journal of Nonlinear Science, 2015.   abstract   arxiv

* G.S. Medvedev, The nonlinear heat equation on dense graphs and graph limits, SIAM J. Math. Analysis, 46(4), 2743-2766, 2014. abstract   pdf

* G.S. Medvedev, The nonlinear heat equation on W-random graphs, Archive for Rational Mechanics and Analysis June 2014, Volume 212, Issue 3, pp 781-803, 2014.   abstract   pdf

* G.S. Medvedev, Small-world networks of Kuramoto oscillators, Physica D 266 (2014), 13-22. abstract   arXiv preprint

* P. Hitczenko and G.S. Medvedev, The Poincare map of randomly perturbed periodic motion, J. Nonlin. Sci., Vol. 23(5), pp. 835-861, 2013. (abstract)

* G.S. Medvedev, Stochastic stability of continuous time consensus protocols, SIAM J. Control Optim., Vol. 50, No. 4, pp. 1859-1885, 2012. PDF

* G.S. Medvedev and S. Zhuravytska, The geometry of spontaneous spiking in neuronal networks, J. Nonlinear Sci., 2012. (abstract)

* G.S. Medvedev, Synchronization of coupled limit cycles, J. Nonlinear Sci., Volume 21, Number 3, pp. 441-464, 2011.


Conferences

Stochastic dynamics out of equilibrium, Insttitut Henri Poincare, Paris, France, June 12-16, 2017


Recent talks

Continuum Limit of the Kuramoto Model on Convergent Graph Sequences, Dynamical Systems Seminar, Kyoto University, July, 2017

Synchronization of coupled systems: Relating network structure to dynamics, Workshop on synchronization and oscillators with generalized coupling, University of Exeter, April 20-22, 2016

The Kuramoto model on Cayley and random graphs, Ohio State University, January 25-29, 2016 (video)


Last modified May 30, 2017.