When the damping is absent, with the increasing of the time-dependent trap asymmetry $\Delta E_{1}$, the sections vary from a single island into a lot of islands, and at last all islands are submerged by the chaotic sea. This means the periodic oscillations become quasi-periodic, and then chaotic. Fig. 5 is the SPS of $(z,dz/dt)$, with $z(0)=0.5$, $\phi (0)=0.0$, $\Delta
E_{0}=0.0$, $\Lambda =10.0$, $\omega =4\pi $ and $\eta =0.0$, for these initial conditions if the damping and the trap asymmetry are absent, the corresponding oscillation is Rabi oscillation. When $\Delta E_{1}=3.000,$ there is only a single island. Then it is separated into six islands when $%
\Delta E_{1}$ increase to $6.000$. For larger trap asymmetry, $\Delta
E_{1}=6.750$, the regular islands are surrounded by the chaotic sea. For large enough trap asymmetry, $\Delta E_{1}=7.500$, the regular islands are all submerged by the chaotic sea, and the sea is symmetrical to $z=0$. Starting from the MQST, the SPS with $z(0)=0.75$, $\phi (0)=0.0$, $\Delta
E_{0}=0.0$, $\Lambda =10.0$, $\omega =2\pi $ and $\eta =0.0$ is showed in Fig. 6, the similar dynamics is exhibited. For small $\Delta E_{1}$ $%
(1.000,1.560$ and $1.565)$, the time-averaged value of the fractional population imbalance is non-zero, the atoms 