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Attractor reconstruction for non-linear systems: a methodological note

Mathematical Biosciences

By:
and
DOI: 10.1016/S0025-5564(01)00053-0

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Abstract

Attractor reconstruction is an important step in the process of making predictions for non-linear time-series and in the computation of certain invariant quantities used to characterize the dynamics of such series. The utility of computed predictions and invariant quantities is dependent on the accuracy of attractor reconstruction, which in turn is determined by the methods used in the reconstruction process. This paper suggests methods by which the delay and embedding dimension may be selected for a typical delay coordinate reconstruction. A comparison is drawn between the use of the autocorrelation function and mutual information in quantifying the delay. In addition, a false nearest neighbor (FNN) approach is used in minimizing the number of delay vectors needed. Results highlight the need for an accurate reconstruction in the computation of the Lyapunov spectrum and in prediction algorithms.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Attractor reconstruction for non-linear systems: a methodological note
Series title:
Mathematical Biosciences
DOI:
10.1016/S0025-5564(01)00053-0
Volume
171
Issue:
1
Year Published:
2001
Language:
English
Contributing office(s):
Patuxent Wildlife Research Center
Description:
21-32
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Mathematical Biosciences
First page:
21
Last page:
32