Date of Award

10-5-2017

Degree Type

Thesis

Degree Name

M.Sc.

Department

Mathematics and Statistics

First Advisor

Caron, Richard

Second Advisor

Gras, Robin

Keywords

chaos, deterministic, Higuchi, optimization, Poincaré, stochastic

Abstract

This thesis is concerned with chaos theory and the analysis of time series using the Poincar e and Higuchi (P&H) method. The P&H method has been shown to qualitatively di erentiate between deterministic and stochastic time series. This thesis proposes that the P&H method can be extended to also quantitatively di erentiate between deterministic and stochastic time series. This extension of the P&H method was tested on twelve time series: six produced by deterministic chaotic systems and six produced by stochastic processes. Results show that, even with noise, the P&H method can quantitatively di erentiate between these two sets of time series. This thesis also studies the problem of optimizing the location of the Poincar e section used in the P&H method. Proposed optimization methods were tested on the same twelve time series. Of the methods tested, the most e ective Poincar e sections were found by a local search method.

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