  As a generic example of a voltage-driven superconducting structure we study a
short superconductor connected to normal leads by means of low transparency
tunnel junctions, with a voltage bias $V$ between the leads. The
superconducting order parameter $\Delta$ is to be determined self-consistently.
We study the stationary states of the system as well as the dynamics after a
perturbation. We find a region in parameter space where there are two stable
stationary states at a given voltage. These bi-stable states are distinguished
by distinct values of the superconducting order parameter $\Delta$ and of the
current between the leads. We have evaluated (1) the multi-valued
superconducting order parameter $\Delta$ at given $V$; (2) the current between
the leads at a given V; and (3) the critical voltage at which superconductivity
in the island ceases. With regards to dynamics, we find numerical evidence that
the stationary states are stable and that no complicated non-stationary regime
can be induced by changing the voltage. This result is somewhat unexpected and
by no means trivial, given the fact that the system is driven out of
equilibrium. The response to a change in the voltage is always gradual, even in
the regime where changing the interaction strength induces rapid anharmonic
oscillations of the order parameter.
