the separatrix solution, that is, the initial conditions and physical parameters are very close to the separatrix of the unperturbed symmetric system. In the case of small trap asymmetry $\Delta E$ and small damping $\eta $, they can be looked as perturbations to the symmetric system, from the general theory of nonlinear driven oscillations, the chaotic macroscopic quantum tunneling phenomena appears when the trap asymmetry is time-dependent. For the two interacting condensates with different hyperfine levels in a single harmonic trap, the damping has the form $-\eta dz/dt$, driving from the effective potential in the previous section, the Newtonian equation of the motion for the fractional population imbalance is given as the following Duffing equation. $$\frac{d^{2}z}{dt^{2}}-(\Lambda H-1)z+\frac{\Lambda ^{2}}{2}z^{3}=-\frac{3}{2}%
\Delta E\Lambda z^{2}-\Delta E^{2}z+\Delta EH-{\normalsize \eta }\frac{dz}{dt%
}.$$ In addition to a time-independent trap asymmetry $\Delta E_{0}$, we impose a sinusoidal variation so that we can write the asymmetry term as $\Delta
E=\Delta E_{0}+\Delta E_{1}\sin \omega t$. When the intensity of the laser beam is fixed, varying the laser barrier position can realize this. Writing the trap asmmetry and the damping as following form $$\Delta E=\Delta E_{0}+\Delta E_{1}\sin \omega t=\varepsilon (F_{0}+F_{1}\sin
\omega t) 
\begin{array}{lll}
& , & 
\end{array}
\eta =\varepsilon \mu .$$ 