Date of Award
Mathematics and Statistics
chaos, deterministic, Higuchi, optimization, Poincaré, stochastic
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
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.
Cavers, Jeremy George, "Chaos and Time Series Analysis: Optimization of the Poincaré Section and distinguishing between deterministic and stochastic time series" (2017). Electronic Theses and Dissertations. 7242.