Date of Award

5-2015

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mathematics

Committee Member

Dr. Elena Dimitrova

Committee Member

Dr. Eleanor Jenkins

Committee Member

Dr. Brian Dean

Abstract

It has been widely observed that most deterministic dynamical systems go into chaos for some values of their parameters. There are many ways to measure chaos. One popular way uses Lyapunov exponents. The objective of this thesis is to find the parameter values for a system that determines chaos via the Lyapunov exponents.The paper by Wolf et.al., proposed the frequently used choice of calculating such exponents using Gram-Schmidt orthonormalization process. The work in this thesis centered on coding and verifying their algorithm , as well as using the code to investigate three biological models to find parameters/initial conditions to give chaos. Finally it also considers as future work choosing appropriate sampling algorithms to better understand the parameter space for which we may obtain chaos.

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