Bifurcation and multifractal vibration in dynamics of a high- T c superconducting levitation system

The vibration of a permanent magnet levitated upon a high- T c superconductor shows chaotic motion under external disturbances. The dynamics depends on the nonlinear force-displacement relation between the permanent magnet and the superconductor, which is related to the magnetic characteristics of the superconductor. In the system two typical routes to chaotic motion are found, from the period doubling sequences and from the bifurcation of quasi-periodic vibrations. Especially in the latter route, multifractality appears in the critical state of chaotic motion that is found in the case of a dissipative system. In this paper, the multifractal vibration of a high- T c superconducting levitation system is experimentally discussed by estimating the singular point spectrum.