离散混沌系统的小波模型和定量分析

A New Wavelet Model for Identification of Discrete Chaotic Systems and Qualitative Analysis of Model

本文对一类离散混沌系统提出一种新的多分辨小波模型 .利用小波时频局域化特性确定最初的小波模型 ,根据匹配寻优准则选择最小的模型结构 .模型的降维分解结构消除了张量积构造多维小波基在高维空间中的“维数灾”问题 .仿真研究不仅表明了该方法辨识混沌系统的有效性 ,还计算了模型的动态不变量 。

This paper develops a new multiresolution wavelet model for a special class of nonlinear system―discrete chaotic system.Based on the time frequency localization properties of wavelet,an initial model is obtained.To obtain a parsimonious dynamical reconstruction,the structure selection algorithm based on match pursuit algorithm is implemented.Lowering dimension decomposition method is proposed to solve the computational cost by the tensor product in high input dimensions.Simulation examples not only show the efficiency of the proposed method,but also compute dynamical invariants of model that is close to those of the original system.