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

Dynamical systems frequently visit the neighborhood of a semistable attract or prior to moving toward that of the nearest locally stable attractor. Sem istable attractors will occur in any system that can have a stable attracto r, 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 t hat the observation of a system near a semistable attractor implies a chang e 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. (C) 1999 Elsevier Science B.V. All rights reserved.