1 March 1994 Experimental test of methods of reconstruction and dimensional analysis of noisy chaotic data sets
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Abstract
The amount of information obtainable from a real dynamical system is limited by the presence of noise, hence noise-reduction techniques are important in all fields in which time-varying signals exist. This paper investigates the use of two such techniques in attractor reconstruction and analysis using time series recorded from a real dynamical system, one involving singular value decomposition and the other Neymark decomposition. The latter was found to have a number of advantages over the former: specifically, it permitted a more reliable estimate of effective embedding dimension, and when used in conjunction with the Grassberger-Procaccia algorithm to measure correlation dimension, it permitted more rapid calculation convergence and also seemed less sensitive to any residual noise or saturation in the time series. The application of both methods will be described, and the advantages claimed for the Neymark decomposition technique substantiated using actual experimental data.
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Una M. Smart, J. C. Earnshaw, "Experimental test of methods of reconstruction and dimensional analysis of noisy chaotic data sets", Proc. SPIE 2037, Chaos/Nonlinear Dynamics: Methods and Commercialization, (1 March 1994); doi: 10.1117/12.167535; https://doi.org/10.1117/12.167535
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