CCMS Colloquium: Shriya Nagpal (Pitzer)

CCMS Colloquium invites you to a talk by Shriya Nagpal (Pitzer)

Abstract: Networks of coupled Kuramoto oscillators have been used to model a wide array of phenomena, including circadian rhythms, flashing fireflies, and high-voltage electric grids. In many such applications, synchronization is an emergent behavior of interest. Recent work has focused on understanding synchronization in random networks of Kuramoto oscillators. We contribute to this literature, by considering interaction networks generated by a graphon model known as a $W$-random network, and examine the dynamics of an infinite number of identical ​ Kuramoto oscillators. We show that with sufficient regularity on $W$, the solution to the dynamical system over a $W$-random network of size $n$ converges to the solution of the infinite graphon system, with high probability as $n\rightarrow\infty$. We leverage this convergence result to study synchronization for identical Kuramoto oscillators on Erd\H{o}s-R\’enyi random graphs.