The information contained in a scalar time series and its time derivatives is used to obtain a global model for the underlying dynamics. This model provides a description of the time evolution of the system studied in a space spanned by the time series and its successive time derivatives which is expected to be equivalent to the original phase space. Differential models are, in general, very complicated and do not necessarily capture all properties of the original dynamics. The possibility of choosing a form among an ansatz library for the original system which allows a structure selection for the differential model is considered. It allows for the reduction of the complexity of the model and the recovery of the right property when the differential model is transformed back into the space associated with the ansatz.

• Received 12 May 2000

DOI:https://doi.org/10.1103/PhysRevE.64.016206