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math.DS2017
The mean field equation for the Kuramoto model on graph sequences with non-Lipschitz limit
Dmitry Kaliuzhnyi-Verbovetskyi, Georgi S. Medvedev
The Kuramoto model (KM) of coupled phase oscillators on graphs provides the most influential framework for studying collective dynamics and synchronization. It exhibits a rich repe…
math.DS2016★ 38 cited
The semilinear heat equation on sparse random graphs
Dmitry Kaliuzhnyi-Verbovetskyi, Georgi S. Medvedev
Using the theory of -graphons (Borgs et al, 2014), we derive and rigorously justify the continuum limit for systems of differential equations on sparse random graphs. Specific…