ABSTRACT

Nonchaotic attractors generally are points, cycles, or smooth surfaces (corresponding to static, periodic, and multifrequency systems, respectively). Their geometry is regular. Small initial errors or minor perturbations generally don't have significant long-term effects. (We saw this in following the routes of various trajectories as they went to a point-or limit-cycle attractor.) Also, neighboring trajectories stay close to one another. Predictions of a trajectory's motion on nonchaotic attractors therefore are fairly meaningful and useful, in spite of errors or differences in starting conditions. Now, just the opposite characteristics describe chaotic attractors, which I'll defme as attractors within the chaotic regime (but see next paragraph). As of yet, there isn't any universal agreement on a definition of a chaotic attractor.