In the above, $\varepsilon $ is a dimensionless parameter. Using the analytical approach developed by us \[20,21\], we write the solution close to the separatrix solution as the following expansions $$z=\sum\limits_{i=0}^{+\infty }\varepsilon ^{i}z_{^{i}}=z_{_{0}}+\varepsilon
z_{_{1}}+\varepsilon ^{2}z_{_{2}}+...$$ Here, $z_{^{i}}$ are the $i-th$ order corrections. Substituting the above expression into the Newtonian equation of the motion, comparing the coefficient function of every $\varepsilon ^{i}$ of both sides of the differential equation, setting $\varepsilon $ as $1$, then we obtain $%
z_{^{i}}$ satisfy $$\frac{d^{2}z_{0}}{dt^{2}}-(\Lambda H-1)z_{0}+\frac{\Lambda ^{2}}{2}%
z_{0}^{3}=0.$$ $$\frac{d^{2}z_{i}}{dt^{2}}-(\Lambda H-1)z_{i}+\frac{3\Lambda ^{2}}{2}%
z_{0}^{2}z_{i}=\epsilon _{i},$$ $$\epsilon _{_{1}}=-\eta \frac{dz_{_{0}}}{dt}+\Delta EH-\frac{3}{2}\Delta
E\Lambda z_{0}^{2},\epsilon _{_{2}}=-\eta \frac{dz_{_{1}}}{dt}-3\Delta
E\Lambda z_{_{0}}z_{_{1}}-\frac{3}{2}\Lambda
^{^{2}}z_{_{0}}z_{_{1}}^{^{2}},...$$ The zero-order solution is the separatrix solution, and the basic solutions of the high-order corrections are as follows $$z_{i1}^{0}=\frac{dz_{0}}{dt}=-\frac{2(\Lambda H-1)}{\sqrt{\Lambda ^{2}}}\sec
h\xi \tanh \xi .$$ $$\begin{aligned}
z_{i2}^{0} &=&z_{i1}^{0}\int (z_{i1}^{0})^{-2}dt  \nonumber \\
&=&\frac{-\sqrt{\Lambda ^{2}}}{16(\Lambda H-1)^{3/2}}\sec h^{2}\xi (\cosh
3\xi -9\cosh \xi +12\xi \sinh \xi ).\end{aligned}$$ So the general expressions of $i-th$ corrections are in form of $$z_{i}=z_{i2}^{0}\int\limits_{C_{1}}^{t}z_{i1}^{0}\epsilon
_{i}dt-z_{i1}^{0}\int\limits_{C_{2}}^{t}z_{i2}^{0}\epsilon _{i}dt.$$ Constants $C_{1}$ and $C_{2}$ are determined by the initial conditions and physical parameters. Apparently, $\left| z_{i1}^{0}\right| \rightarrow 0$ and $\left| z_{i2}^{0}\right| \rightarrow +\infty $, when time $t\rightarrow
\pm \infty $. Solving the $i-th$ order equations one by one, we can obtain $%
\epsilon _{i}$ 