  Bose-Einstein condensates loaded in one-dimensional bichromatic optical
lattices with constituent sublattices having incommensurate periods is
considered. Using the rational approximations for the incommensurate periods,
we show that below the mobility edge the localized states are distributed
nearly homogeneously in the space and explore the versatility of such
potentials. We show that superposition of symmetric and anti-symmetric
localized can be used to simulate various physical dynamical regimes, known to
occur in double-well and multi-well traps. As examples, we obtain an
alternative realization of a bosonic Josephson junction, whose coherent
oscillations display beatings or switching in the weakly nonlinear regime,
describe selftrapping and four-mode dynamics, mimicking coherent oscillations
and self-trapping in four-well potentials. These phenomena can be observed for
different pairs of modes, which are localized due to the interference rather
than due to a confining trap. The results obtained using few-mode
approximations are compared with the direct numerical simulations of the
one-dimensional Gross-Pitaevskii equation. The localized states and the related
dynamics are found to persist for long times even in the repulsive condensates.
We also described bifurcations of the families of nonlinear modes, the symmetry
breaking and stable minigap solitons.
