  The stability and chaotic behaviors of Bose-Einstein condensates with two-
and three-atom interactions in optical lattices are discussed with analytical
and numerical methods. It is found that the steady-state relative population
appears tuning-fork bifurcation when the system parameters are changed to
certain critical values. In particular, the existence of three-body interaction
not only transforms the bifurcation point of the system but also affects
greatly on the macroscopic quantum self-trapping behaviors of the system
associated with the critically stable steady-state solution. In addition, we
also investigated the influence of the initial conditions, three-body
interaction and the energy bias on the macroscopic quantum self-trapping.
Finally, by applying the periodic modulation on the energy bias, we find that
the relative population oscillation exhibits a process from order to chaos, via
a series of period-doubling bifurcations.
