Reconstruction of the vector fields of continuous dynamical systems from numerical scalar time series

We emphasize that the ordinary differential equations of a continuous dynamical system, or at least of equivalent systems, can be reconstructed from numerical scalar time series. Methods are exemplified in the case of a strange, chaotic attractor generated by a mathematical model, namely, a Rössler band. Resultant validations rely (i) qualitatively on comparisons between original and reconstructed phase portraits, and (ii) quantitatively on comparisons between generalized dimensions ${\mathit{D}}_{\mathit{q}}$ of original and reconstructed attractors. Some of the many lines of research offered by the presented results are discussed to stress potentialities of this kind of reconstruction.