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Title:Stability thresholds for signed Laplacians on locally-connected networks
Author(s):Cong, Lin
Director of Research:DeVille, Lee
Doctoral Committee Chair(s):Bronksi, Jared
Doctoral Committee Member(s):Kirkpatrick, Kay; Rapti, Zoi
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):graph Laplacian
dynamics on graphs
Abstract:In this work we are interested in the stability bifurcations of the dynamical systems defined on graphs, and we use signed graph Laplacians as our tool. In chapter 1, we give the formal definition of the Laplacian matrix for a graph, and point out several references on it. In chapter 2, we give the main result from one of the references, along with other preliminaries we need for our results. In chapter 3, we give our first main result -- finding the stable point for the Laplacians of one family of graphs, namely $\mathcal{C}_n^2$. In chapter 4, we extend the previous definition and question to $\mathcal{C}_n^{(k)}$, and we give the exact result for $k=3$, along with a procedure to find the answer for general $k>3$. We then give several conjectures about this topic, which are supported by numerical experiments.
Issue Date:2017-04-19
Type:Thesis
URI:http://hdl.handle.net/2142/97363
Rights Information:Copyright 2017 Lin Cong
Date Available in IDEALS:2017-08-10
Date Deposited:2017-05


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