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.affiliation: BLTP, JINR, Dubna, Moscow Region 141980, Russia.
authors.forename: Yu M
authors.initials: YM
authors.lastname: Shukrinov
authors.affiliation: Department of Physics, University of South Africa, Science Campus, Private Bag X6, Florida Park 1710, South Africa.
authors.forename: A E
authors.initials: AE
authors.lastname: Botha
authors.affiliation: BLTP, JINR, Dubna, Moscow Region 141980, Russia.
authors.forename: S Yu
authors.initials: SY
authors.lastname: Medvedeva
authors.affiliation: Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan, Iran.
authors.forename: M R
authors.initials: MR
authors.lastname: Kolahchi
authors.affiliation: Department of Electrical and Electronic Systems Engineering, Utsunomiya University, 7-1-2 Yoto, Utsunomiya 321-8585, Japan.
authors.forename: A
authors.initials: A
authors.lastname: Irie