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Classifying and quantifying basins of attraction. (English) Zbl 1374.37026

Summary: A scheme is proposed to classify the basins for attractors of dynamical systems in arbitrary dimensions. There are four basic classes depending on their size and extent, and each class can be further quantified to facilitate comparisons. The calculation uses a Monte Carlo method and is applied to numerous common dissipative chaotic maps and flows in various dimensions.{
©2015 American Institute of Physics}

MSC:

37B25 Stability of topological dynamical systems
37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.)

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