Fractal structure of the complete devil’s staircase in dissipative systems described by a driven damped-pendulum equation with a distorted potential

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Abstract
The universality of the fractal structure of the complete devil’s staircase found for a driven damped-pendulum equation is tested against distortion of the potential. The fractal dimension is found to be independent of the exact form of the potential. The different decay exponents for the step sequences 1/Q, the Fibonacci, and P/Q averaged over P are also found to be independent of the potential. The detailed behavior of the I-V curves can, however, be appreciably affected. Nonetheless, the step widths found along the critical line still form a self-similar staircase very nearly symmetric around the 1/2 step. The results mean that the universality may be studied in systems such as Josephson tunnel junctions with external resistive shunts, microbridges, or SNS junctions with external capacitive shunts, Josephson point contacts, or sliding charge-density-wave systems.