多变量时间序列最大Lyapunov指数的噪声估计

在Rosenstein等人研究工作的基础上，提出了一种计算多变量混沌时间序列最大Lyapunov指数的改进的小数据量算法。以Ikeda映射、Henon映射、Lorenz映射和Chen映射四种典型混沌系统为例，采用将随机数方法生成的高斯白噪声与多变量混沌时间序列叠加的方法，分析了相同信噪比下，数据量对最大Lyapunov指数的影响；以及不同信噪比下，混沌时序最大Lyapunov指数的变化趋势。研究结果表明：当加入一定范围信噪比的噪声时，多变量时间序列的最大Lyapunov指数受到的扰动影响很小。

Noise estimates of largest Lyapunov exponents from multivariate time series

On the basis of the work of Rosenstein et al,an improved algorithm is proposed to calculate the largest Lyapu- nov exponent from multivariate chaotic time series.This paper demonstrates the performance for various examples using data from Ikeda map,Henon map, Lorenz map and Chen map,which are contaminated with noise.The multivariate time series are produced by a superposition of Gauss white noise generated by random number and noise-free data in this paper, and also analyzes effects of different noise levels to the largest Lyapunov exponent.The conclusion implies that the effects of noise are not obvious when SNR is in given scope.