Wavelet reconstruction of nonlinear dynamics
D. Allingham, M. West, and A. I. Mees
International Journal of Bifurcation and Chaos 8(11), 2191-2201, 1998.
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.
Full text: AlWeMe1998.pdf