基于时序的李亚普诺夫指数谱的计算

Estimating the Lyapunov Exponent Spectrum from Time Series

讨论了系统模型未知时李亚普诺夫指数谱的计算问题。在已知单个时序的条件下，利用非线性回归方法得到了一个与已知系统同构的系统，设计了一种估计系统参数的稳健的递推算法，以此实现李亚谱诺夫指数谱的计算，数值结果证明了这种方法的可行性。

The Lyapunov expone nt spectrum is an effective tool for judging whether a nonlinearsystem is chaotic. This paper discusses the estimation of Lyapunov exponent spectrum whenthe system model is unknown.Anew method has been developed for the condition that onlyone-dimension time series of an observable variable of a multi-dimension svstem is known.This method is based on the observable 1-D scries and the nonlinear regression estimate isused to construct a homomorphic system in which the first n maximum Lyapunov exponentsare equal to the Lyapunov cxponents of a given system. Numerical results are given.