  Based on the mean-field approximation and the phase space analysis, we
discuss the dynamics of Bose-Einstein condensates in a double-well potential.
By applying a periodic modulation to the coupling between the condensates, we
find the condensates can be trapped in the time-dependent eigenstates of the
effective Hamiltonian, we refer to this effect as time-dependent self-trapping
of BECs. A comparison of this self-trapping with the adiabatic evolution is
made, finding that the adiabatic evolution beyond the traditional(linear)
adiabatic condition can be achieved in BECs by manipulating the nonlinearity
and the ratio of the level bias to the coupling constant. The fixed points for
the system are calculated and discussed.
