Reconstruction of vector fields: The case of the Lorenz system

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Abstract
Ordinary differential equations of continuous dynamical systems, or at least of equivalent systems, can be reconstructed from numerical scalar time series. Corresponding methods have been previously discussed for a Rössler band. This paper is devoted to the case of the Lorenz system. Several kinds of equivalent systems are being investigated, and a classification of them is being introduced. Validations may rely (i) qualitatively with comparisons between graphical displays of exact and corresponding reconstructed attractors and (ii) quantitatively with comparisons between invariants such as generalized dimension spectra.