Abstract The dimension of the Duffing—Holmes two-well potential strange attractor has been measured using both numerical solutions and experimental data from chaotic vibrations of a buckled beam. Using numerical simulation, the fractal dimension of the Poincare section of the strange attractor has been calculated as a function of damping using a correlation function technique. The dimension of the Poincare 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 Poincare section. An analytical expression for the dimension as a function of damping is proposed. The dimension algorithm is applied to experimentally generated Poincare maps from chaotic vibrations of a buckled beam. The calculation yields a dimension of the Poincare map between one and two and seems to be insensitive to the phase of the Poincare section.
[1]
R. A. Mahaffey.
Anharmonic oscillator description of plasma oscillations
,
1976
.
[2]
M. Dubois,et al.
Dimension of strange attractors : an experimental determination for the chaotic regime of two convective systems
,
1983
.
[3]
P. Holmes,et al.
A nonlinear oscillator with a strange attractor
,
1979,
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.
[4]
P. Grassberger,et al.
Characterization of Strange Attractors
,
1983
.
[5]
F. Moon.
Experiments on Chaotic Motions of a Forced Nonlinear Oscillator: Strange Attractors
,
1980
.
[6]
Philip Holmes,et al.
Strange Attractors and Chaos in Nonlinear Mechanics
,
1983
.
[7]
Philip Holmes,et al.
A magnetoelastic strange attractor
,
1979
.
[8]
James P. Crutchfield,et al.
Low-dimensional chaos in a hydrodynamic system
,
1983
.