Reconstruction of standard and inverse vector fields equivalent to a Rössler system

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Abstract
Ordinary diffential equations of continuous dynamical systems, or at least of equivalent systems, can be reconstructed from numerical scalar time series. Methods are exemplified for a Rössler 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
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