Global vector field reconstruction for dynamical systems

When a dynamical system is studied, one of the most interesting goals is to obtain a set of differential equations which provides a model of its behavior. Indeed, it has been pointed out that the knowledge of a global model which captures all the underlying dynamics provides a significant step in the understanding of physical processes. In the case of experiments, the aim is therefore to obtain a set of ordinary differential equations which generates a behavior equivalent to the experimental one starting from a scalar time series given for an observable. The method, the so-called global vector field reconstruction, is described as well as exemplified on experimental cases arising from chemistry, namely a copper electrodissolution and a Belousov-Zhabotinskii reaction. Numerical examples for taking into account a control parameter or for modelling a driven system are also discussed.