The aim of the present work is to investigate the possibility to retrieve the original sets of dynamical equations directly from observational time series when all the system variables are observed. Time series are generated from chosen dynamical systems, and the global modeling technique is applied to obtain optimal models of parsimonious structure from these time series. The obtained models are then compared to the original equations to investigate if the original equations can be retrieved. Twenty-seven systems are considered in the study. The Rössler system is first used to illustrate the procedure and then to test the robustness of the approach under various conditions, varying the initial conditions, time series length, dynamical regimes, subsampling (and resampling), measurement noise, and dynamical perturbations. The other 26 systems (four rational ones included) of various algebraic structures, sizes, and dimensions are then considered to investigate the generality of the approach.
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February 2019
Research Article|
February 25 2019
Can the original equations of a dynamical system be retrieved from observational time series?
Sylvain Mangiarotti
;
Sylvain Mangiarotti
Centre d’Études Spatiales de la Biosphère, UPS-CNRS-CNES-INRA-IRD, Observatoire Midi-Pyrénées
, 18 avenue Édouard Belin, 31401 Toulouse, France
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Mireille Huc
Mireille Huc
Centre d’Études Spatiales de la Biosphère, UPS-CNRS-CNES-INRA-IRD, Observatoire Midi-Pyrénées
, 18 avenue Édouard Belin, 31401 Toulouse, France
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Chaos 29, 023133 (2019)
Article history
Received:
November 14 2018
Accepted:
February 01 2019
Citation
Sylvain Mangiarotti, Mireille Huc; Can the original equations of a dynamical system be retrieved from observational time series?. Chaos 1 February 2019; 29 (2): 023133. https://doi.org/10.1063/1.5081448
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