Chaos and Time Series Analysis: Optimization of the Poincare Section And Distinguishing Between Deterministic and Stochastic Time Serie

This thesis is concerned with chaos theory and the analysis of time series using the Poincare and Higuchi (P&H) method. The P&H method has been shown to qualitatively differentiate between deterministic and stochastic time series. This thesis proposes that the P&H method can be extended to also quantitatively differentiate 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 differentiate between these two sets of time series.;This thesis also studies the problem of optimizing the location of the Poincare section used in the P&H method. Proposed optimization methods were tested on the same twelve time series. Of the methods tested, the most effective Poincare sections were found by a local search method.