A comparison of polynomial and wavelet expansions for the identification of chaotic coupled map lattices

摘要

A comparison between polynomial and wavelet expansions for the identification of coupled map lattice (CML) models for deterministic spatiotemporal dynamical systems is presented in this paper. The pattern dynamics generated by smooth and nonsmooth nonlinear maps in a well-known two-dimensional CML structure are analyzed. By using an orthogonal feed forward regression algorithm (OFR), polynomial and wavelet models are identified for the CML's in chaotic regimes. The quantitative dynamical invariants such as the largest Lyapunov exponents and correlation dimensions are estimated and used to evaluate the performance of the identified models.