NDLI: Generalized Theorems for Nonlinear State Space Reconstruction

Content Provider	PubMed Central
Author	Deyle, Ethan R. Sugihara, George
Editor	Oresic, Matej
Abstract	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.
Related Links	http://dx.doi.org/10.1371/journal.pone.0018295
Starting Page	18295
File Format	PDF
ISSN	19326203
e-ISSN	19326203
Journal	PLoS ONE
Issue Number	3
Volume Number	6
Language	English
Publisher	Public Library of Science
Publisher Date	2011-03-31
Access Restriction	Open
Rights Holder	Public Library of Science
Subject Keyword	Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Multidisciplinary

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