Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, April 17, 2019.

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events for the
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Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, April 17, 2019

4:00 pm in 245 Altgeld Hall,Wednesday, April 17, 2019

#### From Graph Laplacian to the Stability of Coupled Oscillator Networks

###### Lan Wang (Illinois Math)

Abstract: There is a large amount of applied problems that can be posed as dynamical systems on a coupled oscillator network. Frequently these problems involve computing the inertia of a graph Laplacian. In this talk we will start with an overview of the properties of the Laplacian matrix and then explore how it functions in the study of the stability of fixed points of dynamical systems. Particularly, we will discuss the Kuramoto model, a classic and popular model for describing the dynamics of a large population of coupled oscillators. We will first deliberate the stability of the phase-locked solutions of Kuramoto model on single-layer networks, and then extend it to multi-layer networks by examining the Supra-Laplacian matrix.