Attractor reconstruction for non-linear systems: a methodological note
Mathematical Biosciences
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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.
Suggested Citation
Nichols, J., and Nichols, J., 2001, Attractor reconstruction for non-linear systems: a methodological note: Mathematical Biosciences, v. 171, no. 1, p. 21-32, https://doi.org/10.1016/S0025-5564(01)00053-0.
| 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 |