The fractal dimension of the two-well potential strange attractor
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.
scientific article; zbMATH DE number 3944905