  The phase dynamics of Josephson junctions under external electromagnetic
radiation is studied through numerical simulations. Current-voltage
characteristics, Lyapunov exponents and Poincare 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
Josephson junction 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.
