基于重采样的混沌时间序列相空间重构研究

相空间重构是混沌时间序列分析中的重要一步,本文在总的观测时间确定的情况下,研究了重采样对混沌时间序列相空间重构的影响,提出了一种确定重采样间隔的双对数图法。模型实验及初步的理论证明表明,通过选择合适的重采样间隔进行相空间重构,重构相空间的基本结构和形状不会改变,且保持了原相空间的各种重要特性。此外带来的另一优点是计算复杂度的大大降低,这为应用较短的时间序列进行相空间重构以及计算各种不变量提供了一种可行有效的方法。

A Resampling Based Phase Space Reconstruction for Chaotic Time Series

In the reconstruction of phase space, the length of time series affects the quality of reconstruction phase space directly. To reconstruct phase space accurately, the length of time series must be very long, especially for the continuous chaotic systems. On the condition of keeping the total observation time constant, the method of resampling is applied to the chaotic time series, and the experimental results and corresponding analysis indicate that resampling can keep the good enough quality of original phase space, and reduce the total time of computation quickly. This may be a good method to reconstruct phase space by short time series and an efficient way to compute the invariants of chaotic system.