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.
Yu.M.S. thanks I. Rahmonov, M. Yu. Kupriyanov, K. Y. Constantinian, G. A. Ovsyannikov, and V. P. Koshelets for helpful discussions and D. V. Kamanin and the JINR-SA agreement for the support of this work. He also appreciates kind hospitality of Professor Y. Takayama and Professor N. Suzuki from Utsunomiya university where part of this work was done. Yu.M.S. and M.R.K. wish to thank the Physics Department at the University of South Africa for a pleasant stay.
I. INTRODUCTION II. SUBHARMONIC STEPS III. STRUCTURED CHAOS IV. BACKBONE FEATURES AND FAREY SUM RULE V. CHAOS ON THE SUBHARMONIC STEPS OF THE SVETLANA A. Demonstration of Feigenbaum period doubling scenario B. Universality in the sequence of periodic windows C. On-step positive Lyapunov exponent VI. DEPENDENCE OF SVETLANA ON RADIATION AND JJ PARAMETERS VII. REVIEWING THE EXPERIMENTAL RESULTS VIII. CONCLUSION