Then the total energy density can be written as $\rho=\rho_\phi+\rho_\gamma$, with the energy density of scalar field $\rho_\phi=\frac12\dot{\phi}^2+V(\phi)$ and the energy density of barotropic fluid $\rho_\gamma$. We consider that the energy momenta of this field to be covariant conserved. Then one has $$\begin{aligned}
&&\ddot{\phi}+3H\dot{\phi}+V'=0,\label{ddotphi}\\
&&\dot{\rho}_\gamma+3\gamma H\rho_\gamma=0, \label{dotrg}\end{aligned}$$ where $\gamma$ is an adiabatic index and satisfies $p_\gamma=(\gamma-1)\rho_\gamma$ with $p_\gamma$ being the pressure of the barotropic fluid, and the prime denotesthe differentiation with respect to the field $\phi$. Differentiating Eq. (\[Fri\]) and using Eqs. (\[ddotphi\]) and (\[dotrg\]), one can obtain $$\begin{aligned}
\dot{H}=-\frac12\left(\dot{\phi}^2+\gamma\rho_\gamma\right)\left[1-\frac{2(\rho_\gamma+\rho_\phi)}{\rho_c}\right].
\label{Fri4}\end{aligned}$$

Equations (\[Fri\])-(\[dotrg\]) and (\[ddotphi\])-(\[Fri4\]) characterize a closed system which can determine the cosmic behavior. To analyze the dynamical behavior of the Universe, one can further introduce the following variables [@Copeland-exponential; @Samart-Phantom]: $$\begin{aligned}
x\equiv\frac{\dot{\phi}}{\sqrt{6}H},\quad
y\equiv\frac{\sqrt{V}}{\sqrt{3}H},\quad
z\equiv\frac{\rho}{\rho_c},\quad \lambda\equiv\frac{V'}{V},
\label{new-v}\end{aligned}$$ where the $z$ term is a special variable in LQC \[see Eq. (\[Fri\])\]. In the LQC scenario, the total energy density $\rho$ should be less than or equal to the critical energy density $\rho_c$, and thus $0\leq z\leq 1$. Notice that, in the classical region, $z=0$ for $\rho\ll\rho_c$. Using these new variables, one can obtain $$\begin{aligned}
&&\frac{\rho_\gamma}{3H^2}=\frac{1}{1-z}-x^2-y^2,\label{rg-xyz}\\
&&\frac{\dot{H}}{H^2}=-\left[3x^2+\frac{3\gamma}{2}\left(\frac{1}{1-z}-x^2-y^2\right)\right]\left(1-2z\right)\nonumber\\
\label{dH-HH}.\end{aligned}$$

Using the new variables (\[new-v\]), and considering Eqs. (\[rg-xyz\]) and (\[dH-HH\]), one can 