  We present effects of an external driving on the tunneling dynamics of
interacting bosons confined in a double well potential. At large values of a
periodic driving potential, the dynamics become chaotic, with a distinct
difference between tuning of the amplitude or the phase of the driving term
with regard to the route leading to chaos. For example, we find that a
controlled increase in the amplitude of the driving term with a fixed phase
leads to quasiperiodic route to chaos. While tuning of the frequency with a
fixed (large) amplitude leads to a crisis induced intermittency route to a
chaotic dynamics, where the system intermittently visits different attractors
in the phase space. Surprisingly, a chirp frequency superposed on a harmonic
signal suppresses the chaotic motion, thereby yielding an orderly dynamics,
pretty similar to a (damped) Rabi oscillation.
