  Motivated by recent experiments, where a voltage biased Josephson junction is
placed in series with a resonator, the classical dynamics of the circuit is
studied in various domains of parameter space. This problem can be mapped onto
the dissipative motion of a single degree of freedom in a nonlinear
time-dependent potential, where in contrast to conventional settings the
nonlinearity appears in the driving while the static potential is purely
harmonic. For long times the system approaches steady states which are analyzed
in the underdamped regime over the full range of driving parameters including
the fundamental resonance as well as higher and sub-harmonics. Observables such
as the dc-Josephson current and the radiated microwave power give direct
information about the underlying dynamics covering phenomena as bifurcations,
irregular motion, up- and down conversion. Due to their tunability, present and
future set-ups provide versatile platforms to explore the changeover from
linear response to strongly nonlinear behavior in driven dissipative systems
under well defined conditions.
