Modeling Chaos

Abstract

We next discuss making models for prediction or control of the source of the observed chaotic signal. In a sense this is both the easiest and the hardest task we have discussed. It is the easiest because it is quite simple to make models of the dynamics which very accurately allow one to predict forward in time from any new initial condition close to or on the attractor within the limits of the intrinsic instabilities embodied in the positive Lyapunov exponents. It is also the hardest because there is no guideline as to which of many functional forms to use for the models and what interpretation to place on the parameters in the models from a physical point of view. In this section we make models on the attractor and evaluate them by how well they do in prediction or possibly prediction of Lyapunov exponents.