×

Wavelet reconstruction of nonlinear dynamics. (English) Zbl 0984.37102

Summary: We investigate the reconstruction of embedded time-series from chaotic dynamical systems using wavelets. The standard wavelet transforms are not applicable because of the embedding, and we use a basis pursuit method which on its own does not perform very well. When this is combined with a continuous optimizer, however, we obtain very good models. We discuss the success of this method and apply it to some data from a vibrating string experiment.

MSC:

37M10 Time series analysis of dynamical systems
65T60 Numerical methods for wavelets
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Cao L., Phys. 85 pp 225– (1995)
[2] DOI: 10.1007/BF01010828 · Zbl 0588.58041
[3] Judd K., Phys. 82 pp 426– (1995)
[4] Judd K., Phys. 92 pp 221– (1996)
[5] DOI: 10.1109/78.258082 · Zbl 0842.94004
[6] Marquardt D. W., J. SIAM 11 pp 431– (1963)
[7] DOI: 10.1109/PROC.1987.13849
[8] DOI: 10.1016/0022-460X(90)90796-3
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.