Generalized theorems for nonlinear state space reconstruction.
Generalized theorems for nonlinear state space reconstruction.
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DOI：
10.1371/journal.pone.0018295
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发表时间：
2011-03-31
期刊：
影响因子：
3.7
通讯作者：
Sugihara G
中科院分区：
文献类型：
--
作者：
Deyle ER;Sugihara G
Takens定理（1981）表明了如何将单个时间序列的滞后变量用作代理变量，以重建潜在动态过程的吸引子。单时间序列的状态空间重构（SSR）是分析自然界和人类世界中普遍存在的复杂非线性系统的一种有效方法。这些方法的主要缺点是吸引子重建的唯象性质。此外，应用研究表明，这些单一的时间序列重建往往可以通过在重建中包括多个动态耦合的时间序列来改进，以提供更机械的模型。在这里，我们提供了三个分析证明，增加了越来越多的文献，以推广Takens的工作，并演示了如何多个时间序列可以用于吸引子重建。这些扩展的结果（Takens定理是一个特例）适用于各种各样的自然系统，具有并行的时间序列观测变量被认为是相关的相同的动态流形。由不同变量组合（及其滞后）创建的多个嵌入提供的潜在信息杠杆可以为新的应用技术铺平道路，以利用自然系统的时间有限但并行的观测，如耦合生态系统，地球物理系统和金融系统。本文旨在证明并帮助开辟自然科学中SSR应用的这一潜在增长领域。
Takens' theorem (1981) shows how lagged variables of a single time series can be used as proxy variables to reconstruct an attractor for an underlying dynamic process. State space reconstruction (SSR) from single time series has been a powerful approach for the analysis of the complex, non-linear systems that appear ubiquitous in the natural and human world. The main shortcoming of these methods is the phenomenological nature of attractor reconstructions. Moreover, applied studies show that these single time series reconstructions can often be improved ad hoc by including multiple dynamically coupled time series in the reconstructions, to provide a more mechanistic model. Here we provide three analytical proofs that add to the growing literature to generalize Takens' work and that demonstrate how multiple time series can be used in attractor reconstructions. These expanded results (Takens' theorem is a special case) apply to a wide variety of natural systems having parallel time series observations for variables believed to be related to the same dynamic manifold. The potential information leverage provided by multiple embeddings created from different combinations of variables (and their lags) can pave the way for new applied techniques to exploit the time-limited, but parallel observations of natural systems, such as coupled ecological systems, geophysical systems, and financial systems. This paper aims to justify and help open this potential growth area for SSR applications in the natural sciences.
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影响因子：
8.6
作者：
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通讯作者：
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影响因子：
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作者：
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影响因子：
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作者：
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作者：
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通讯作者：
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DOI：
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发表时间：
2007-06-01
影响因子：
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