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

Abstract

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.

Authors:
 [1];  [1];  [2];  [3]
  1. BLTP, JINR, Dubna, Moscow Region 141980 (Russian Federation)
  2. Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan (Iran, Islamic Republic of)
  3. Department of Electrical and Electronic Systems Engineering, Utsunomiya University, 7-1-2 Yoto, Utsunomiya 321-8585 (Japan)
Publication Date:
OSTI Identifier:
22351138
Resource Type:
Journal Article
Journal Name:
Chaos (Woodbury, N. Y.)
Additional Journal Information:
Journal Volume: 24; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1054-1500
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; COMPUTERIZED SIMULATION; ELECTRIC POTENTIAL; ELECTROMAGNETIC RADIATION; FRACTALS; JOSEPHSON JUNCTIONS; LYAPUNOV METHOD; PERIODICITY

Citation Formats

Shukrinov, Yu. M., Botha, A. E., E-mail: bothaae@unisa.ac.za, Medvedeva, S. Yu., Moscow Institute of Physics and Technology, Kolahchi, M. R., and Irie, A. Structured chaos in a devil's staircase of the Josephson junction. United States: N. p., 2014. Web. doi:10.1063/1.4890573.
Shukrinov, Yu. M., Botha, A. E., E-mail: bothaae@unisa.ac.za, Medvedeva, S. Yu., Moscow Institute of Physics and Technology, Kolahchi, M. R., & Irie, A. Structured chaos in a devil's staircase of the Josephson junction. United States. doi:10.1063/1.4890573.
Shukrinov, Yu. M., Botha, A. E., E-mail: bothaae@unisa.ac.za, Medvedeva, S. Yu., Moscow Institute of Physics and Technology, Kolahchi, M. R., and Irie, A. Mon . "Structured chaos in a devil's staircase of the Josephson junction". United States. doi:10.1063/1.4890573.
@article{osti_22351138,
title = {Structured chaos in a devil's staircase of the Josephson junction},
author = {Shukrinov, Yu. M. and Botha, A. E., E-mail: bothaae@unisa.ac.za and Medvedeva, S. Yu. and Moscow Institute of Physics and Technology and Kolahchi, M. R. and Irie, A.},
abstractNote = {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.},
doi = {10.1063/1.4890573},
journal = {Chaos (Woodbury, N. Y.)},
issn = {1054-1500},
number = 3,
volume = 24,
place = {United States},
year = {2014},
month = {9}
}