Nonlinear Dynamics and Statistics (eBook)

All models are lies. "e;The Earth orbits the sun in an ellipse with the sun at one focus"e; is false, but accurate enough for almost all purposes. This book describes the current state of the art of telling useful lies about time-varying systems in the real world. Specifically, it is about trying to "e;understand"e; (that is, tell useful lies about) dynamical systems directly from observa- tions, either because they are too complex to model in the conventional way or because they are simply ill-understood. B(:cause it overlaps with conventional time-series analysis, building mod- els of nonlinear dynamical systems directly from data has been seen by some observers as a somewhat ill-informed attempt to reinvent time-series analysis. The truth is distinctly less trivial. It is surely impossible, except in a few special cases, to re-create Newton's astonishing feat of writing a short equation that is an excellent description of real-world phenomena. Real systems are connected to the rest of the world; they are noisy, non- stationary, and have high-dimensional dynamics; even when the dynamics contains lower-dimensional attractors there is almost never a coordinate system available in which these at tractors have a conventionally simple description.