MTO 604E - Nonlinear Time Series Analysis

Course Objectives

The main purpose of this course is to reconstruct the phase space by using a time series in order to estimate the underlying dynamics that produces the time series in question.

Course Description

Dynamical systems and chaos. Characterization of dynamical systems: Autocorrelation function, Mutual information function, power spectrum, Lyapunov exponents, Poincaré section, fractal dimensions. Dimension algorithms. Determinism in time series: Reconstruction of phase space, choosing delay time, determination of embedding and attractor dimensions. Noise reduction in phase space. Prediction of chaotic time series. Reconstruction of differential equations from time series.