&=&[E_{2}+U_{2}\left| \psi
_{_{2}}\right| ^{2}]\psi _{_{2}}-K\psi _{_{1}}.\end{aligned}$$ Where, $E_{1}$ and $E_{2}$ are zero-point energies in each well, $%
U_{1}\left| \psi _{_{1}}\right| ^{2}$ and $U_{2}\left| \psi _{_{2}}\right|
^{2}$ are proportional to the atomic self-interacting energies, and $K$ describes the amplitude of the tunneling between two condensates. These parameters are defined by the overlap integrals of the time-dependent Gross-Pitaevsky eigenfunctions. The above equations are named as BJJ equations, which have been derived from GPE in reference \[17\].

The wave function $\psi _{i}$ can be written in the form of $\psi _{_{i}}=%
\sqrt{N_{i}}\exp (i\theta _{i})$, here, $N_{i\text{ }}$and $\theta _{i}$ are the amplitudes for general occupations and phases respectively. Then the fractional population imbalance can be defined as $$z(t)=\frac{N_{1}(t)-N_{2}(t)}{N_{T}}=\frac{\left| \psi _{_{1}}\right|
^{2}-\left| \psi _{_{2}}\right| ^{2}}{\left| \psi _{_{1}}\right| ^{2}+\left|
\psi _{_{2}}\right| ^{2}}.$$ here, $N_{T}=N_{1}(t)+N_{2}(t)$ is a constant total number of condensed atoms. And the relative phase is $$\phi (t)=\theta _{2}(t)-\theta _{1}(t).$$ Then the fractional population imbalance and the relative phase obey the following differential equations $$\begin{aligned}
\frac{dz}{dt} &=&-\frac{2K}{\hbar }\sqrt{1-z^{2}}\sin \phi ,  \nonumber \\
\frac{d\phi }{dt} &=&\frac{2K}{\hbar }(\Delta E+\Lambda z+\frac{z}{\sqrt{%
1-z^{2}}}\cos \phi ).\end{aligned}$$ The parameters $\Delta E$ and $\Lambda $ determine the dynamic regimes of the BEC atomic tunneling and they can be expressed as $$\Delta 