Evaluation of Lyapunov exponents and scaling functions from time series

Abstract

An algorithm to calculate the Lyapunov exponents from an experimental time series is discussed and tested on simulated data of various nonlinear systems. It is applied to the analysis of experiments on a parametrically modulated nuclear magnetic resonance laser system, and the results are compared with the values of the dimensions and entropies determined by different methods. The distribution of the Lyapunov exponents and the corresponding scaling function is discussed.