标量时间序列时滞的不完全相空间方法
Incomplete Phase-Space Method to Reveal Time Delay From Scalar Time-series
摘要：
提出了一种计算速度快、概念简单的从标量时间序列中恢复混沌系统时延的方法。我们发现，在不完整的二维重构相空间中的轨道将显示局部聚类现象后，在这项工作中提出的组件置换程序。我们发现，由不完整的二维重构相空间捕获的信息与系统中存在的时延${τ_0}$有关，并通过分量置换过程传递给置换分量。然后，我们提出了分段均值方差（SMV）从置换成分来识别系统的时间延迟${τ_0}$。当不完全重构的嵌入延迟$τ$与混沌系统的时间延迟${τ_0}$匹配时，SMV具有明显的最大值.基于Mackey-Glass方程在混沌状态下运行的时滞系统所产生的数值数据被用来说明所提出的SMV的有效性。实验结果表明，该方法对观测噪声具有较强的鲁棒性，即使在数据量较小、反馈强度较弱的情况下，也能恢复混沌系统的时延.此外，该方法的时间复杂度是相当低的。
英文摘要：
A computationally quick and conceptually simple method to recover time delay of the chaotic system from scalar time series is developed in this paper. We show that the orbits in the incomplete two-dimensional reconstructed phase-space will show local clustering phenomenon after the component permutation procedure proposed in this work. We find that information captured by the incomplete two-dimensional reconstructed phase-space, is related to the time delay ${τ_0}$ present in the system, and will be transferred to the permutation component by the procedure of component permutation. We then propose the segmented mean-variance (SMV) from the permutation component to identify the time delay ${τ_0}$ of the system. The proposed SMV shows clear maximum when the embedding delay $τ$ of the incomplete reconstruction matches the time delay ${τ_0}$ of the chaotic system. Numerical data generated by a time-delay system based on the Mackey-Glass equation operating in the chaotic regime are used to illustrate the effectiveness of the proposed SMV. Experimental results show that the proposed SMV is robust to additive observational noise and is able to recover the time delay of the chaotic system even though the amount of data is relatively small and the feedback strength is weak. Moreover, the time complexity of the proposed method is quite low.
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