Phase portraits from a time series: A singular system approach

Abstract

We review a singular system approach, developed during the past three years at the Royal Signals and Radar Establishment, to the reconstruction and analysis of phase portraits obtained from time series data. We show how the singular system approach is used to obtain optimum global coordinates for the phase portrait, and then how the approach is used to conduct a local analysis of the dynamical system. The local analysis is applied to the calculation of the topological dimension of the manifold of an experimental chaotic dynamical system. The results of this calculation point to a difficulty in the usual implementation of fractal dimension calculations.