多变量时间序列最大李雅普诺夫指数的计算

Calculation of the maximal Lyapunov exponent from multivariate data

根据单变量时间序列计算最大Lyapunov指数的算法思想,本文提出了一种于多变量时间序列最大Lyapunov指数计算的方法.针对原有算法需要使用重构相空间的特点,推广算法给出了多变量时间序列相空间重构参数的选择方法,并采用多变量重构相空间进行最大Lyapunov指数计算.经耦合R ssler系统产生多变量时间序列的仿真计算,验证了该算法的有效性,推广算法的计算结果表明多变量时间序列的计算结果优于单变量的结果,且更加接近理论计算结果.

According to the method of calculating maximal Lyapunov exponent （MLE） from univariate small data sets, an extended method based on multivariate time series is proposed. The extended method can search out optimal reconstructing parameters to meet the requirement of the original method for reconstructing multivariate phase space, and the method can compute the MLE by making use of the optimal reconstructed multivariate phase space. The method is tested by coupled non-identical chaotic Rtissler, coupled chaotic Roessler and hyper chaotic Roessler. The test results show that the extend method is efficient, and the computing results of MLE based on multivariate are much closer to the theoretical values than the results of univariate even when the data sets of each time series become small.