IDENTIFICATION AND PREDICTION OF LOW DIMENSIONAL DYNAMICS

This contribution focuses upon extracting information from dynamic reconstructions of experimental time series data. In addition to the problem of distinguishing between deterministic dynamics and stochastic dynamics, applied questions, such as the detection of parametric drift, are addressed. Nonlinear prediction and dimension algorithms are applied to geophysical laboratory data, and the significance of these results is established by comparison with results from similar surrogate series, generated so as not to contain the property of interest. A global nonlinear predictor is introduced which attempts to correct systematic bias due to the inhomogeneous distribution of data common in attractors. Variations in the quality of predictions with location in phase space are examined in order to estimate the uncertainty in a forecast at the time it is made. Finally, the application of these methods to truly stochastic systems is discussed and the distinction between deterministic, stochastic, and low dimensional dynamics is considered.