  The problem of nonlinear transport in a two dimensional superconductor with
an applied oscillating electric field is solved by the holographic method. The
complex conductivity can be computed from the dynamics of the current for both
near- and non-equilibrium regimes. The limit of weak electric field corresponds
to the near equilibrium superconducting regime, where the charge response is
linear and the conductivity develops a gap determined by the condensate. A
larger electric field drives the system into a superconducting non-equilibrium
steady state, where the nonlinear conductivity is quadratic with respect to the
electric field. Keeping increasing the amplitude of applied electric field
results in a far-from-equilibrium non-superconducting steady state with a
universal linear conductivity of one. In lower temperature regime we also find
chaotic behavior of superconducting gap, which results in a non-monotonic field
dependent nonlinear conductivity.
