Classifying and quantifying basins of attraction

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 2015 English Publisher:AIP PublishingJournal:Chaos: An Interdisciplinary Journal of Nonlinear Science, volume 25 (issn: 1054-1500, eissn: 1089-7682,

Copyright policy )

Authors: J. C. Sprott; Anda Xiong;

doi: 10.1063/1.4927643

pmid: 26328552

Classifying and quantifying basins of attraction

- Summary
- Subjects
- Metrics

Abstract

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.

Related Organizations

University of Wisconsin–Madison
United States
University of Wisconsin–Oshkosh
United States

Keywords

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

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	71
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%