A unified and automated approach to attractor reconstruction

We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful...

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Bibliographic Details
Published inNew journal of physics Vol. 23; no. 3; p. 33017
Main Authors Kraemer, K H, Datseris, G, Kurths, J, Kiss, I Z, Ocampo-Espindola, J L, Marwan, N
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.03.2021
Subjects
Automation
complex systems
Cost function
Embedding
nonlinear dynamics
Optimization
Oscillators
Parameters
Physics
Reconstruction
state space reconstruction
Time lag
Time series
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Summary:We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data from chaotic chemical oscillators.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/abe336