A Chaotic Global Modeling Method Based on Orthogonal Polynomials

JIAN Xiang-chao; ZHENG Jun-li

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A Chaotic Global Modeling Method Based on Orthogonal Polynomials

更新时间：2025-07-16

- A Chaotic Global Modeling Method Based on Orthogonal Polynomials
- Acta Electronica Sinica Vol. 30, Issue 1, Pages: 76-78(2002)
- 作者机构：
  
  清华大学电子工程系,北京,100084
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN914
- Published：2002
- 稿件说明：
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JIAN Xiang-chao, ZHENG Jun-li. A Chaotic Global Modeling Method Based on Orthogonal Polynomials[J]. Acta Electronica Sinica, 2002, 30(1): 76-78.
DOI：

JIAN Xiang-chao, ZHENG Jun-li. A Chaotic Global Modeling Method Based on Orthogonal Polynomials[J]. Acta Electronica Sinica, 2002, 30(1): 76-78. DOI：

摘要

本文研究了一种正交多项式混沌全局建模方法

所用正交多项式集以吸引子不变测度为核.通过对Hénon映射数据和电离层参数实测数据的分析

表明在待建模系统不很复杂时(其内在机理可用较低阶多项式表达)

这种全局建模方法能得到系统动力学特性.在低噪声情况下模型还能充分精确地重构系统方程式.在噪声较大或系统内在机理很复杂时建模结果仍可用于一步预测

且具有较好效果.

Abstract

In this article

we study a chaotic global modeling method based on a set of polynomials defined on the attractor's invariant measure as its kernel.Through analysis of Hénon map data and observed data of ionospheric parameters

it is shown that if the underlying system is simple enough to be represented by low-order polynomials

this method can capture the dynamics of the system.Also

when the noise level is low

we can acquire the equation of the system.When noise level is higher or the system is more complex

we still can use the reconstructed model to perform one-step prediction in a fairly good fashion.

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