Discrete Wavelet Models for Identification and Qualitative Analysis for Chaotic Systems

This paper develops a new approach for identifying nonlinear representations of chaotic systems directly from noise-corrupted data. The nonlinear functional describing the process is constructed using a new multiresolution model structure implemented with B-spline wavelet and scaling functions.Following an iterative strategy, a sequence of model sets of increasing complexity are postulated and tested until a suitable model is found. An orthogonal-forward-regression routine coupled with model validity tests is used to select parsimonious wavelet models and to measure the quality of the fit. The effectiveness of the identification procedure is demonstrated using both simulated and experimental data. It is shown that the proposed method can produce accurate models which exhibit qualitatively the same dynamical behaviour as the observed system and are characterised by dynamical invariants which are very close to those of the original system.