Decay of metastable states with discrete dynamics

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Abstract
We consider the escape from invariant sets of one-dimensional piecewise linear maps which are additively disturbed by weak Gaussian white noise. The escape rates from point attractors and from strange invariant sets in the vicinity of the crisis at fully developed chaos are analytically determined and compared with results from numerical simulations. Both situations are combined resulting in a model with a point attractor which has a strange invariant set as basin boundary. Numerically a nonexponential decay of the attractor is found that can be described by a Markovian three-state model with transition rates known from the previous analysis.

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