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Experimental Techniques

 

The dynamics of a forced string raises experimental challenges common to a variety of nonlinear systems. In this section we describe a few of the experimental diagnostics that help with the visualization and identification of different attractors, such as:

equilibrium points
limit cycles (periodic orbits)
invariant tori (quasiperiodic orbits)
strange attractors (chaotic orbits)

The main tools used in the real-time identification of an attractor are Fourier power spectra and real-time Poincaré maps. In addition, the correlation dimension calculated from an experimental time series helps to confirm the existence of a strange attractor, as well as providing a measure of its fractal structure.

The terms ``strange attractor'' and ``chaotic attractor'' are not always interchangeable. Specifically, a strange attractor  is an attractor that is a fractal . That is, the term strange refers to a static geometric property of the attractor. The term chaotic attractor  refers to an attractor whose motions exhibit sensitive dependence on initial conditions. That is, the term chaotic refers to the dynamics on the attractor. We mention this distinction because it is possible for an attractor to be strange (a fractal), but not chaotic (exhibit sensitive dependence on initial conditions) [25]. Experimental methods are available for quantifying both the geometric structure of an attractor (fractal dimensions) and the dynamic properties of orbits on an attractor (Lyapunov exponents).





Nicholas B. Tufillaro
Mon Mar 3 01:58:02 PST 1997