## Files in this item

FilesDescriptionFormat

application/pdf

CONG-DISSERTATION-2017.pdf (455kB)
(no description provided)PDF

## Description

 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
﻿