Georgi Medvedev

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  The Kuramoto model on Cayley and random graphs
  Georgi Medvedev
  In this talk, I will discuss the continuum limit for coupled dynamical systems on large graphs and applications to stability of spatial patterns in the Kuramoto model of coupled phase oscillators.
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  Synchronization of coupled systems: Relating network topology to dynamics
  Georgi Medvedev
  We will discuss dynamics in two representative models of dynamical systems on graphs: coupled chaotic maps and coupled excitable systems driven by white noise. For both models, we analyze synchronization and explain what structural features of the network favor synchronization. For the second model, we also describe other dynamical regimes such as spontaneous oscillations and formation of clusters. The role of network topology in shaping each of these patterns will be explained.