Numerical Procedures for Analyzing Dynamical Processes

摘要

We are delivering a tape with a software package for UNIX workstations withdocumentation for analyzing low dimensional dynamical behavior from time series. In particular, the Lyapunov exponent code will, together with the dimension code, permit the user to distinguish between periodic, chaotic, and random processes. 'Random processes' here means behavior whose dimension is too high to compute. The code computes the information dimension of the time series. We are also including in the same tape a noise-reduction code with documentation. We have developed a method which we believe is a potential breakthrough in the analysis of experimental data. Typically, attractors are reconstructed from a scalar time series of experimental data using time delays. Conventional signal filtering techniques are not useful in this case, because they examine only portions of the signal which are close in time.