MODELING AND SYNCHRONIZING CHAOTIC SYSTEMS FROM EXPERIMENTAL-DATA

The inverse problem of extracting evolution equations from chaotic tim e series measured from continuous systems is considered. The resulting equations of motion form an autonomous system of nonlinear ordinary d ifferential equations (ODEs). The vector fields are modeled in the man ner of implicit Adams integration using a basis set of polynomials tha t are constructed to be orthonormal on the data. The fitting method us es the Rissanen minimum description length (MDL) criterion to determin e the optimal polynomial vector field. It is then demonstrated that on e can synchronize the model to an experimentally measured time series. In this case synchronization is used as a nontrivial test for the val idity of the models.