Zhang J, Luo X, Small M
Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jan;73(1 Pt 2):016216. doi: 10.1103/PhysRevE.73.016216. Epub 2006 Jan 24.
A different method is proposed to detect deterministic structure from a pseudoperiodic time series. By using the correlation coefficient as a measure of the distance between cycles, we are exempt from phase-space reconstruction and further construct a hierarchy of pseudocycle series that, in turn, preserve less determinism than the original time series. Appropriate statistics are then devised to reveal the temporal and spatial correlation encoded in this hierarchy of the pseudocycle series, which allows for a reliable detection of determinism and chaos in the original time series. We demonstrate that this method can reliably identify chaos in the presence of noise of different sources for both artificial data and experimental time series.
本文提出了一种从伪周期时间序列中检测确定性结构的不同方法。通过使用相关系数作为周期之间距离的度量，我们无需进行相空间重构，并进一步构建了伪周期序列的层次结构，而该层次结构所保留的确定性比原始时间序列要少。然后设计了适当的统计量来揭示编码在该伪周期序列层次结构中的时间和空间相关性，这使得能够可靠地检测原始时间序列中的确定性和混沌。我们证明，对于人工数据和实验时间序列，该方法在存在不同来源噪声的情况下都能可靠地识别混沌。
