Classifying and Quantifying Basins of Attraction

J. C. Sprott and Anda Xiong
Physics Department, University of Wisconsin - Madison, 1150 University Avenue, Madison, Wisconsin 53706, USA

Received 16 April 2015; accepted 20 July 2015; published online 3 August 2015


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.

Ref: J. C. Sprott and A. Xiong, Chaos 25, 083101-1 - 083101-7 (2015)

The complete paper is available in PDF format.

Return to Sprott's Books and Publications.