for different values of $\Lambda $ with fixed value of $H$.

The motion in the parabolic potential is Rabi oscillation with a zero time-average value of the fractional population imbalance $z$. For fixed parameters $\Lambda $ and $H$, the oscillations with small effective energies $H_{eff\text{ }}$are sinusoidal, the increasing of the effective energies adds higher harmonics to the sinusoidal oscillations.

In the case of double-well potential, the motion is very different from the case of the parabolic potential. If the effective energies is greater than the barrier between two wells, that is, $H_{eff}>0$, the motion is a nonlinear Rabi oscillation with a zero time-average value of $z$, it corresponds to the periodic flux of atoms from one BEC to the other. If the effective energy is little than the potential barrier, $H_{eff}<0$, the particle is confined in one of the two wells, it means the localization of atomic population in one of the two condensates, and this localizing phenomenon has been named as macroscopic quantum self-trapping (MQST). At the threshold point, the effective energy is equal to the potential barrier, $H_{eff}=0$, the corresponds threshold motion separating the above two regimes, the separatrix solution for the right-hand side well is $$z_{s}(t)=2\sqrt{(\Lambda 