RECONSTRUCTION OF THE VECTOR-FIELDS OF CONTINUOUS DYNAMIC-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 Rossler band. Resultant validations rely (i) qualitatively on comparisons between original and reconstructed phase portraits, and (ii) quantitatively on comparisons between generalized dimensions D(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.