RECONSTRUCTION OF STANDARD AND INVERSE VECTOR-FIELDS EQUIVALENT TO A ROSSLER SYSTEM

Ordinary diffential equations of continous dynamical systems, or at least of equivalent systems, can be reconstructed from numerical scalar time series. Methods are exemplified for a Rossler band. Equivalent systems are standard and inverse systems, which are systematically investigated. Validations rely (i) qualitatively on comparisons between phase portraits and (ii) quantitatively on comparisons between generalized dimension spectra. By-products of the work are an information-compression scheme for time-series encoding and the introduction of squeezed systems that facilitate evaluations of generalized dimensions of small order q < 1.