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Stability assessment methods for dynamical systems have recently beencomplemented by basin stability and derived measures, i.e. probabilisticstatements whether systems remain in a basin of attraction given a distributionof perturbations. This requires numerical estimation via Monte-Carlo samplingand integration of differential equations. Here, we analyze the applicabilityof basin stability to systems with basin geometries challenging for thisnumerical method, having fractal basin boundaries and riddled or intermingledbasins of attraction. We find that numerical basin stability estimation isstill meaningful for fractal boundaries but reaches its limits for riddledbasins with holes.

Potentials and Limits to Basin Stability Estimation