一种计算有限时间Lyapunov指数的新方法及仿真研究

A Quickly Converging and Numerically Stable Method of Calculating Finite Time Lyapunov Exponents(FTLEs) of Multidimensional System with Degenerate Spectrum

Lyapunov指数(LEs)是反映混沌系统动力学特性的一个重要定量指标,如何有效快速地计算LEs成为混沌信号处理中的一个基本问题。Goldhirsch,Sulen和Orszag在标准QR法基础上提出了一种修正方法,该方法对计算非退化谱有效,但是对计算(伪)退化谱不够精确。该文在Goldhirsch等人的方法基础上,给出一种新的计算有限时间Lyapunov指数(FTLEs)方法,对标准映射和Henon映射进行了数值仿真。结果表明,该方法具有更快的收敛速度和更好的稳定性。

We found that the method of Goldhirsch et al for calculating FTLEs is unsatisfactory for multidimensional system with degenerate spectrum. In the full paper, we explain in detail the mathematics of generalizing their method to make it applicable to the case of degenerate spectrum. We give two simulation examples; they both show preliminarily that, compared with the method of Goldhirsch et al, our proposed new method is quickly converging and stable for calculating FTLEs in the case of degenerate spectrum.