Influence of Measured Time Series in the Reconstruction of Nonlinear Multivariable Dynamics

In this chapter, we will try to point out the important problem of the choice of a time series to study a dynamical system. Indeed, it has been shown that, in spite of Takens’ theorem which states that an equivalent space may be obtained from any general observing function, there are usually some variables that allow a better representation of the underlying dynamics. In other words, when only a single scalar time series can be recorded, the choice of the variable or a given quantity evolving with respect to time is crucial in the modeling and analysis of the dynamics underlying the data. We will give different illustrative examples for which representation of the dynamics is biased by the choice of the variable.