Choice of dynamical variables for global reconstruction of model equations from time series

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Abstract
The success of modeling from an experimental time series is determined to a significant extent by the choice of dynamical variables. We propose a method for preliminary investigation of a time series whose purpose is to find out whether a global dynamical model with smooth functions can be constructed for the chosen variables. The method consists in the estimation of single valuedness and continuity of relations between dynamical variables and variables to enter left-hand sides of model equations. The method is explained with numerical examples. Its efficiency is demonstrated by modeling a real nonlinear electric circuit.