Exploiting properties of semistable attractors to predict change in non-linear systems

Dynamical systems frequently visit the neighborhood of a semistable attractor prior to moving toward that of the nearest locally stable attractor. Semistable attractors will occur in any system that can have a stable attractor, and come into existance when a stable attractor has been destabilised by a change in one or more system parameters. The difficulty this raises is that the observation of a system near a semistable attractor implies a change in the state of the system at some future time. The question is, can the time when this change occurs be predicted. We here show that the answer to this question is affirmative. While the existance of semistable attractors creates this problem, the statistical properties of dwell times provide the means of solving it.