  We study the classical dynamics of an axion field (the signal) that is
coupling into a Josephson junction (the detector) by means of a capacitive
coupling of arbitrary size. Depending on the size of the coupling constant and
the initial conditions, we find a rich phase space structure of this nonlinear
problem. We present general analytic solutions of the equations of motion in
the limit of small amplitudes of the angle variables, and discuss both the case
of no dissipation and the case of dissipation in the system. The effect of a
magnetic field is investigated as well, leading to topological phase
transitions in the phase space structure.
