Electronic Thesis and Dissertation Repository

Degree

Master of Science

Program

Applied Mathematics

Supervisor

Dr. Geoff Wild

Abstract

Chaos is the seemingly irregular behavior arising from a deterministic system. Chaos is observed in many real-world systems. Edward Lorenz’s seminal discovery of chaotic behavior in a weather model has prompted researchers to develop tools that distinguish chaos from non-chaotic behavior. In the first chapter of this thesis, I survey the tools for detecting chaos namely, Poincaré maps, Lyapunov exponents, surrogate data analysis, recurrence plots and correlation integral plots. In chapter two, I investigate blood pressure fluctuations for chaotic signatures. Though my analysis reveals interesting evidence in support of chaos, the utility such an analysis lies in a different direction that I point to the reader. In chapter three, I investigate a simulation of predator-prey interactions. My analysis casts doubt on some of the claims laid by past researchers, and I prompt future researchers to probe some specific questions that I have outlined in this thesis.

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