Author ORCID Identifier

Date of Award

Summer 8-8-2023

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics

First Advisor

Igor Belykh

Second Advisor

Michael Stewart

Third Advisor

Yaroslav Molkov

Fourth Advisor

Vladimir Bondarenko


This thesis presents several novel results on the nonlinear and emergent collective dynamics of crowds and populations in complex systems. Though, historically, the list of suspension bridges destabilized by pedestrian collective motion is long, the phenomenon still needs to be fully understood, especially regarding the effect of human-to-human interactions on the structure, and often incorrectly explained using synchronization theory. We present a simple general formula that quantifies the effect of pedestrian effective damping of a suspension bridge and illustrate it by simulating three mathematical models, including one with a strong propensity for synchronization. Despite the subtle effects of gait strategies in determining precise instability thresholds, our results show that average negative damping is always the trigger of pedestrian-induced high-amplitude lateral vibration of suspension bridges. Furthermore, we show that human-to-human interactions of heterogeneous pedestrians can trigger the instability of a bridge more effectively than crowds of identical pedestrians. We will also discuss the role of crowd heterogeneity in possible phase pulling between pedestrians and bridge motion. We also develop a model for the evolution of toxic memes on 4chan and report a significant influence on Twitter’s anti-vaccine conspiracy discourse over a nine-year period. We show that 4chan topics evolve according to an emergent process mathematically similar to classic reinforcement learning methods, tending to maximize the expected toxicity of future discourse. We demonstrate that these topics can invade Twitter and persist in an endemic state corresponding to the associated spreading rate and initial distribution of post rates and coexisting with a higher-traffic regime of dynamics. We discuss the implication of this result for preventing large-scale disinformation campaigns.


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