A unified and automated approach to attractor reconstruction

Krämer, Kai-Hauke; Datseris, George; Kurths, Jürgen; Kiss, Istvan Z.; Ocampo-Espindola, Jorge L.; Marwan, Norbert

doi:10.1088/1367-2630/abe336

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A unified and automated approach to attractor reconstruction

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Krämer, Kai-Hauke
Potsdam Institute for Climate Impact Research;

Datseris, George
External Organizations;

/persons/resource/Juergen.Kurths

Kurths, Jürgen
Potsdam Institute for Climate Impact Research;

Kiss, Istvan Z.
External Organizations;

Ocampo-Espindola, Jorge L.
External Organizations;

/persons/resource/Marwan

Marwan, Norbert
Potsdam Institute for Climate Impact Research;

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Zitation

Krämer, K.-H., Datseris, G., Kurths, J., Kiss, I. Z., Ocampo-Espindola, J. L., Marwan, N. (2021): A unified and automated approach to attractor reconstruction. - New Journal of Physics, 23, 3, 033017.
https://doi.org/10.1088/1367-2630/abe336

Zitierlink: https://publications.pik-potsdam.de/pubman/item/item_25381

Zusammenfassung

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.