Dissertation/Thesis Abstract

Continuum Limit and Synchronization Conditions for Coupled Oscillators on Lattices
by Wu, Tianqi, Ph.D., New York University, 2019, 56; 13421111
Abstract (Summary)

Kuramoto oscillators coupled through a graph provide one of the most influential models for the study of collective synchronizations. We propose the first sufficient synchronization conditions for lattice models. This sufficient condition is optimal as an L synchronization condition. We also propose a novel continuum limit of the Kuramoto oscillators on lattices, by viewing the lattice as a discretization of the space. In the continuous model we have an analogous synchronization condition. To prove the continuous (discrete) synchronization conditions, we show the existence of solutions to some (discrete) elliptic PDE of divergence form. The two main ingredients in the proof are variational methods and gradient estimates for (discrete) elliptic PDE's.

Indexing (document details)
Advisor: Young, Lai-Sang
Commitee: Bakhtin, Yuri, Gunturk, Sinan, Kohn, Robert V., Luo, Feng, Serfaty, Sylvia
School: New York University
Department: Mathematics
School Location: United States -- New York
Source: DAI-B 80/08(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Continuous synchronization, Discretization of the space, Kuramoto oscillators
Publication Number: 13421111
ISBN: 9781392004623
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