By Boone Fleenor

Faculty Mentor: Leo Lee

Abstract

In this thesis, we develop and analyze two nonlinear systems of ordinary differential equations to model Bitcoin price dynamics. Analytical techniques are used to obtain exact or approximate solutions where possible. Then, numerical simulations using a fourth-order Runge–Kutta method are employed to explore system behavior beyond analytically tractable regimes. Finally, model outputs are compared to historical Bitcoin price data using normalized and resampled time series. These results suggest that deterministic models can provide meaningful insight into the structural behavior of Bitcoin markets, while highlighting the need for stochastic or time-dependent extensions for more realistic modeling.