Structured chaos in a devil's staircase of the Josephson junction

The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters a...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2014-09, Vol.24 (3), p.033115-033115
Main Authors: Shukrinov, Yu M, Botha, A E, Medvedeva, S Yu, Kolahchi, M R, Irie, A
Format: Article
Language:English
Subjects:
CHAOS THEORY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Computer simulation
COMPUTERIZED SIMULATION
Current voltage characteristics
ELECTRIC POTENTIAL
ELECTROMAGNETIC RADIATION
FRACTALS
JOSEPHSON JUNCTIONS
Liapunov exponents
LYAPUNOV METHOD
Parameters
Period doubling
PERIODICITY
Regression analysis
Staircases
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Summary:The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.4890573