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: Korman 222
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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: Korman 222 |
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 boards of Discrete and Continous Dynamical Systems (Series B) and Networks and Heterogeneous Media.
Dr. Medvedev's research areas include dynamical systems, stochastic analysis, numerical methods, and
mathematical neuroscience. Dr. Medvedev pioneered the use of graphons to study interacting dynamical systems. His recent work focuses on continuum description of
large dynamical networks with applications to synchronization and pattern formation in systems of
coupled oscillators.
Dr. Medvedev's research has been supported by National Science Foundation
through grants
* P. Dupuis and G.S. Medvedev, The large deviation principle for interacting dynamical systems on random graphs, Comm. in Math. Phys., 390, (2022) ( arxiv).
* D. Kaliuzhnyi-Verbovetskyi and G.S. Medvedev, The mean field equation for the Kuramoto model on graph sequences with non-Lipschitz limit, SIAM J. Math. Anal., 50 (2018), no. 3, 2441-2465, abstract pdf
* G.S. Medvedev, The continuum limit of the Kuramoto model on sparse random graphs, Communications in Mathematical Sciences, vol. 17 (2019), no. 4,pp. 883- 898.
* 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, 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, M.S. Mizuhara, A. Phillips, A global bifurcation organizing rhythmic activity in a coupled network, Chaos 32, 083116 (2022)
* H. Chiba, G.S. Medvedev, M.S. Mizuhara, Bifurcations and patterns in the Kuramoto model with inertia, submitted, ( arxiv ).
* H. Chiba and G.S. Medvedev, Stability and bifurcation of mixing in the Kuramoto model with inertia, SIAM J. Math. Anal., 54(2), 2022 ( arxiv ).
* G.S. Medvedev and M. Mizuhara, Chimeras unfolded, J. Stat. Phys., 86, 2022.
* G.S. Medvedev and M. Mizuhara, Stability of Clusters in the Second-Order Kuramoto Model on Random Graphs , J. Stat. Physics, 2021, ( arxiv).
* H. Chiba and G.S. Medvedev, The mean field analysis for the Kuramoto model on graphs I. The mean field equation and transition point formulas, Discrete and Continuous Dynamical Systems - A, 39(1), 2019. ( abstract )
* H. Chiba and G.S. Medvedev, The mean field analysis for the Kuramoto model on graphs II. Asymptotic stability of the incoherent state, center manifold reduction, and bifurcations, Discrete and Continuous Dynamical Systems - A, 39(7), 2019. ( abstract ) arxiv
* H. Chiba, G.S. Medvedev, and M. Mizuhara, Bifurcations in the Kuramoto model on graphs, Chaos 28, 073109 (2018), abstract, arxiv
* G.S. Medvedev and X. Tang, The Kuramoto model on power law graphs: Synchronization and Contrast States, Journal of Nonlinear Science, 2018, abstract arxiv
* 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, Small-world networks of Kuramoto oscillators, Physica D 266 (2014), 13-22.
* G.S. Medvedev and G. Simpson, A Numerical Method for a Nonlocal Diffusion Equation with Additive Noise, Stoch PDE: Anal and Comp, (2022) ( arxiv ).
* D. Kaliuzhnyi-Verbovetskyi and G.S. Medvedev, Sparse Monte Carlo method for nonlocal diffusion equations, SIAM J. Numer. Anal., accepted, arxiv
* 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) (arXiv preprint)
* 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 S. Zhuravytska, The geometry of spontaneous spiking in neuronal networks, J. Nonl. Sci., 2012. ( arXiv:1105.2801).
* G.S. Medvedev, Synchronization of coupled limit cycles, Journal of Nonlinear Science, 2011. PDF
* G.S. Medvedev, Reduction of a model of an excitable cell to a one-dimensional map, Physica D, 202(1-2), 37-59, 2005. ( PDF )
* G.S. Medvedev, J.E. Cisternas, Multimodal regimes in a compartmental model of the dopamine neuron, Physica D, 194(3-4), 333-356, 2004. ( PDF )
International Conference on Difference Equations and Applications, Paris-Saclay, France, July 18-22, 2022.
SIAM Conference on Nonlinear Waves and Coherent Structures, University of Bremen, Germany, August 30 - September 2, 2022.
Graphon Dynamical Systems: a Law of Large Numbers, Large Deviations,
and Metastability,
SIAM Conference on Nonlinear Waves and Coherent Structures,
University of Bremen, Germany, August 30 - September 2, 2022.
Last modified June 11, 2022.
Movies of the patterns generated by the Kuramoto model are available
here.