Graduation Year

2024

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Heather Zinn Brooks

Reader 2

Andrew Bernoff

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Terms of Use for work posted in Scholarship@Claremont.

Rights Information

© 2024 Tian Dong

Abstract

Mathematicians use models of opinion dynamics to describe how opinions in a group of people change over time, which can yield insight into mechanisms behind phenomena like polarization and consensus. In these models, mathematicians represent the community as a graph, where nodes represent agents and edges represent possible interactions. Opinion updates are modeled with a system of differential equations (ODEs). Our work focuses on the sigmoidal bounded confidence model (SBCM), where agents update their opinion toward a weighted average of their neighbors' opinions by weighting similar opinions more heavily. Using tools developed in physics (mean-field theory), we derive a continuity equation from the system of ODEs to further analyze the model's steady states and compare with numerical simulations.

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