ORCID

000900070285544X

Keywords

mathematical models, revolution, misinformation, protests, democratization, autocratization

Abstract

Revolutions, defined by Skocpol as rapid transformations in class, state, and/or social structures, are important world events that can cause civil wars, spark international trends, and result in transitions toward democratic and autocratic regimes alike. They are characterized largely by the mechanism of mass mobilization, which is increasingly facilitated by online networks and digital communication. In this dissertation, we investigate such means and outcomes of revolutions as dynamical systems. We construct three models describing separate but complementary aspects of revolution, beginning at the smallest unit of analysis and then moving outward in scope. First, we construct a graph-based model to investigate how individual accounts in a social network spread information, misinformation, or disinformation as a Markov process. Second, we build a system of ordinary differential equations to describe a compartmental model exploring how a population engages with political demonstrations that are driven in part by such a social network. Third, we consider how governments change over time, due in part to political demonstrations, by modeling governmental shifts as one-dimensional biased random walks informed by real-world data. For each model, we define foundational assumptions that allow us to derive governing equations. We present some limited analytic results for each model, then largely investigate them through numerical implementation. We identify meaningful parameter spaces and examine potential threshold values within those spaces, and finally suggest real-world implications of our results from the perspectives of different actors within each model.

Completion Date

2026

Semester

Spring

Committee Chair

Nevai, Andrew

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Mathematics

Format

PDF

Document Type

Dissertation

Identifier

DP0053146

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