Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Potentials and Limits to Basin Stability Estimation   Stability assessment methods for dynamical systems have recently been
complemented by basin stability and derived measures, i.e. probabilistic
statements whether systems remain in a basin of attraction given a distribution
of perturbations. This requires numerical estimation via Monte-Carlo sampling
and integration of differential equations. Here, we analyze the applicability
of basin stability to systems with basin geometries challenging for this
numerical method, having fractal basin boundaries and riddled or intermingled
basins of attraction. We find that numerical basin stability estimation is
still meaningful for fractal boundaries but reaches its limits for riddled
basins with holes.

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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: chem-ph