Improved Techniques for Modeling and Controlling Nonlinear Systems with FewDegrees of Freedom

摘要

New nonlinear signal processing and modeling techniques were examined. The keyissues which formed the focus of the project: were (1) The design of coupling terms for synchronizing the model with driving signals from the system of interest. This is the first analytical result of its kind, and gives sufficient conditions for guaranteeing that the model will synchronize. (2) The development of symbolic time series methods for estimation of correlation timescales of complex signals and the detection of weak periodicites. (3) A theory of anomalous scaling behavior in nonnomal systems which are subcritical (i.e. linearly stable but unstable to finite amplitude perturbations). Both noise free and noise driven cases were treated.