MODELING AND SYNCHRONIZING CHAOTIC SYSTEMS FROM EXPERIMENTAL-DATA

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