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A practical method for calculating largest Lyapunov exponents from small data sets. (English) Zbl 0779.58030

This paper addresses the problem of calculating the largest Lyapunov exponents of a dynamical system from small sets of experimental data. The authors have devised an algorithm which they claim to be fast, easily implemented, and robust to changes in embedding dimension, size of the data set, reconstruction delay, and noise level.

The current most popular algorithm for quantifying chaotic behavior is the Grassberger-Procaccia method, but this algorithm is sensitive to small variations in parameters, and generally requires long, noise-free time series. The authors of this paper note that calculation of the largest Lyapunov exponents is the most direct method for quantifying chaotic behavior manifested in time series produced by dynamical systems. However, the largest Lyapunov exponent has proven difficult to estimate for small data sets, and existing algorithms to compute it are computationally intensive and difficult to implement. The new algorithm which the authors present is direct and efficient, and is capable of estimating the correlation dimension as well as the largest Lyapunov exponent.

MSC:
37D45Strange attractors, chaotic dynamics