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Sampling period, statistical complexity, and chaotic attractors

机译：采样周期，统计复杂度和吸引子

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摘要

We analyze the statistical complexity measure vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period τ and show that, if the Bandt and Pompe procedure is used to assign a probability distribution function (PDF) to the pertinent time series, the statistical complexity measure (SCM) attains a definite maximum for a specific sampling period ~(tM). On the contrary, the usual histogram approach for assigning PDFs to a time series leads to essentially constant SCM values for any sampling period τ. The significance of ~(tM) is further investigated by comparing it with typical times found in the literature for the two main reconstruction processes: the Takens' one in a delay-time embedding, on one hand, and the exact NyquistShannon reconstruction, on the other one. It is shown that ~(tM) is compatible with those times recommended as adequate delay ones in Takens' reconstruction. The reported results correspond to three representative chaotic systems having correlation dimension 2< ~(D2)<3. One recent experiment confirms the analysis presented here.
机译：我们分析了统计复杂度测度与采样混沌吸引子的熵平面表示随采样周期τ的关系，并表明，如果使用Bandt和Pompe程序将概率分布函数（PDF）分配给相关时间序列，统计复杂性度量（SCM）在特定采样周期〜（tM）内达到一定的最大值。相反，用于将PDF分配给时间序列的常规直方图方法导致任何采样周期τ的SCM值基本恒定。通过将〜（tM）与文献中发现的两个主要重建过程的典型时间进行比较，可以进一步研究〜（tM）的意义：一方面，延迟时间嵌入中的Takens's，另一方面，在精确的NyquistShannon重建中，另外一个。结果表明，〜（tM）与在Takens重建中建议作为适当延迟时间的那些时间兼容。报告的结果对应于三个相关维度为2 <〜（D2）<3的代表性混沌系统。最近的一项实验证实了此处介绍的分析。

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