Autoregressive Methods for Chaos on Binary Sequences for the Lorenz Attractor

摘要

A binary sequence is defined for the Lorenz attractor. This binary sequence contains some information about the original system. To extract this information we have used autoregressive methods from the theory of signal processing. The binary sequences and the associated methods could also be used to estimate the system characteristics when one does not have access to all the variables involved in the underlying process; this is usually the case in an experimental study. We introduce an autocorrelation function for binary sequences, a one-step predictor and associated power spectra and a macroscopic approximation of the largest Lyapunov exponent. Keywords: Reprints, Mathematical prediction. (kr)