The fractal dimension of the two-well potential strange attractor
type: Item
instance of: scholarly article
title: The fractal dimension of the two-well potential strange attractor
zbMATH Open document ID: 0588.58038
DOI: 10.1016/0167-2789(85)90137-X
author: Francis C. Moon
author: Guangxuan Li
published in: Physica D
publication date: 1985-01-01T00:00:00Z
review text: The dimension of the Duffing-Holmes two-well potential strange attractor has been measured using both numerical solutions and experimental data from chaotic vibration of a buckled beam. Using numerical simulation, the fractal dimension of the Poincaré section of the strange attractor has been calculated as a function of damping using a correlation function technique. The dimension of the Poincaré section is between one and two with higher damping resulting in a smaller dimensional attractor. An equivalent Cantor set for the attractor is defined. The dimension seems to be relatively insensitive to the phase of the Poincaré section. An analytical expression for the dimension as a function of damping is proposed. The dimension algorithm is applied to experimentally generated Poincaré maps from chaotic vibrations of a buckled beam. The calculation yields a dimension of the Poincaré map between one and two and seems to be insensitive to the phase of the Poincaré section.
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 3944905
zbMATH Keywords: fractal dimension
zbMATH Keywords: Duffing equation
zbMATH Keywords: damping
zbMATH Keywords: numerical simulation
zbMATH Keywords: chaotic vibration of a buckled beam
reviewed by: J.Šiška
MaRDI profile type: Publication
cites work: A nonlinear oscillator with a strange attractor
cites work: A magnetoelastic strange attractor
full work available at URL: 0167-2789(85)90137-x
OpenAlex ID: W2051793899
description: scientific article; zbMATH DE number 3944905