  We analyze theoretically the role of the exciton-phonon interactions in
phenomena related to the Josephson effect between two spatially separated
exciton and exciton-polariton condensates. We consider the role of the
dephasing introduced by phonons in such phenomena as Josephson tunneling,
self-trapping and spontaneous polarization separation. In the regime of cw
pumping we find a remarkable bistability effect arising from exciton- exciton
interactions as well as regimes of self- sustained regular and chaotic
oscillations.
