An Algorithm for Computing the Largest Lyapunov Exponent Based on Space Grid Method

YANG Ai-bo; WANG Ji; LIU Shu-yong; WEI Xiu-lei

doi:10.3969/j.issn.0372-2112.2012.09.026

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An Algorithm for Computing the Largest Lyapunov Exponent Based on Space Grid Method

更新时间：2025-07-16

- An Algorithm for Computing the Largest Lyapunov Exponent Based on Space Grid Method
- Acta Electronica Sinica Vol. 40, Issue 9, Pages: 1871-1875(2012)
- 作者机构：
  
  海军工程大学船舶与动力学院,湖北,武汉,430033
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.51179197);Fund for State Key Laboratory of Ocean Engineer of Shanghai Jiao Tong University (No.1009)
- DOI：10.3969/j.issn.0372-2112.2012.09.026
  CLC： TN710O415.5
- Published：2012
- 稿件说明：
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YANG Ai-bo, WANG Ji, LIU Shu-yong, et al. An Algorithm for Computing the Largest Lyapunov Exponent Based on Space Grid Method[J]. Acta Electronica Sinica, 2012, 40(9): 1871-1875.
DOI：

YANG Ai-bo, WANG Ji, LIU Shu-yong, et al. An Algorithm for Computing the Largest Lyapunov Exponent Based on Space Grid Method[J]. Acta Electronica Sinica, 2012, 40(9): 1871-1875. DOI： 10.3969/j.issn.0372-2112.2012.09.026.

摘要

最大Lyapunov指数是判断时间序列是否为混沌的一个重要判据

但传统方法求解的计算量很大

所需时间较长

导致在工程实际应用中受到限制.本文提出了基于空间栅格法的最大Lyapunov指数的改进算法

该方法将重构后的整个相空间进行分割

形成多个小空间

搜索邻近点时只需在其子空间内进行搜索

可以大大提高搜索速度.仿真实验表明改进的邻近点搜索方法无论在有噪声情况下还是在无噪声情况下都具有良好的鲁棒性

可以快速而有效地实现参考点邻域的搜索

极大的缩短了计算时间

且易于编程实现

使混沌信号特征指数的在线提取成为了可能.

Abstract

The largest Lyapunov exponent is an essential criterion to judge whether the time series is chaos or not.However

the traditional methods are complex and time-consuing

which leads to the limitations in engineering application.An improved algorithm based on space grid method for estimating the largest Lyapunov exponent is presented.Firstly

the whole reconstructed phase space is divided into small spaces;then the points locating in these subspaces which are searched when the reference point exists;finally

the characteristic exponent is calculated.Simulation results show that neighborhoods are searched effectively

and the whole calculated time is reduced greatly.In practically

the algorithm is robust to reconstructed parameters

noise and data length

and it is easy to be programmed as well

which make exponents computed of chaos online possible.

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Related Institution

Institute of Science,Air Force Engineering University

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