Identification and Reconstruction of Chaotic Systems Using Multiresolution Wavelet Decompositions

A new modelling framework for identifying and reconstructing chaotic systems is developed based on multiresolution wavelet decompositions. Qualitative model validation is used to compare the multiresolution wavelet models and it is shown that the dynamical features of chaotic systems can be captured by the identified models providing the wavelet basis functions are properly selected. Two basis selection algorithms, orthogonal least squares (OLS) and a new matching pursuit orthoganal least squares (MPOLS), are considered and compared. Several examples are included to illustrate the results