  We study the collective dynamics of a driven two mode Bose-Hubbard model in
the Josephson interaction regime. The classical phase-space is mixed, with
chaotic and regular components, that determine the dynamical nature of the
fringe-visibility. For weak off-resonant drive, where the chaotic component is
small, the many-body dynamics corresponds to that of a Kapitza pendulum, with
the relative-phase $\varphi$ between the condensates playing the role of the
pendulum angle. Using a master equation approach we show that the modulation of
the inter-site potential barrier stabilizes the $\varphi=\pi$ 'inverted
pendulum' coherent state, and protects the fringe visibility.
