Stability thresholds for signed Laplacians on locally-connected networks

Cong, Lin

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https://hdl.handle.net/2142/97363 Copy

Description

Title

Stability thresholds for signed Laplacians on locally-connected networks

Author(s)

Cong, Lin

Issue Date

2017-04-19

Director of Research (if dissertation) or Advisor (if thesis)

DeVille, Lee

Doctoral Committee Chair(s)

Bronksi, Jared

Committee Member(s)

• Kirkpatrick, Kay
• Rapti, Zoi

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2017-05

Type of Resource

text

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http://hdl.handle.net/2142/97363

Copyright and License Information

Copyright 2017 Lin Cong

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