Practical Methods of Measuring the Generalized Dimension and the Largest Lyapunov Exponent in High Dimensional Chaotic Systems

Abstract

Practical methods to extract the generalized dimension Dq and the largest Lyapunov exponent from experimental data are proposed and tested on examples. The measured values agree well with known values. In applications to chaotic signals, convergence of dimension is investigated for varying the delay time and the embedding dimension.