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Analysis of Chaotic Data with Mathematica

Heikki Ruskeepää

We present Mathematica programs to analyze chaotic data. The following topics are considered: - delay time (with the method of average mutual information) - embedding dimension (with the method of false nearest neighbors) - correlation dimension (with the method of correlation exponent) - maximal Lyapunov exponent (with the method of local divergence rates) - nonlinear prediction (with the method of analogues) As examples, we consider data derived from the logistic, Hénon, and Lorenz models as well as real NMR laser data.

*Mathematics > Calculus and Analysis > Dynamical Systems
*Science > Physics

chaos, chaotic data, analysis of chaotic data, chaotic data analysis, nonlinear models, delay time, embedding dimension, correlation dimension, maximal Lyapunov exponent, nonlinear prediction, average mutual information, false nearest neighbors, correlation exponent, local divergence rates, method of analogues, logistic model, Hénon model, Lorenz model, NRM laser

i_ Part 1.zip (7.7 MB) - ZIP archive
i_ Part 2.zip (5.2 MB) - ZIP archive
i_ Part 3.zip (6.1 MB) - ZIP archive