and then the dynamical system is reduced from three dimensions to two dimensions.) The cost of this simplification is that the potential of the field is restricted. Recently, Zhou *et al* [@Zhou-plb; @Fang-CQG] considered the potential parameter $\Gamma$ as a function of another potential parameter $\lambda$, which enables one to study the fixed points for a large number of potentials. We will follow this method in this section and the sections that follow to discuss the dynamical behavior of the scalar field in the LQC scenario, and we have $$\begin{aligned}
\Gamma(\lambda)=f(\lambda)+1.\label{G-l}\end{aligned}$$ In this case, Eq. (\[G-l\]) can cover many scalar potentials.

For completeness’ sake, we briefly review the discussion of [@Fang-CQG] in the following. From Eq. (\[l-G\]), one can obtain $$\begin{aligned}
\frac{d\lambda}{\lambda f(\lambda)}=\frac{dV}{V}.\label{l-f-V}\end{aligned}$$ Integrating out $\lambda=\lambda(V)$, one has the following differential equation of potential $$\begin{aligned}
\frac{dV}{V\lambda(V)}=d\phi.\label{l-V}\end{aligned}$$ Then, Eqs. (\[l-f-V\]) and (\[l-V\]) provide a route for obtaining the potential $V=V(\phi)$. If we consider a concrete form of the potential (e.g., an exponential potential), the dynamical system is specialized (e.g., the dynamical system is reduced to three dimensions if one considers the exponential potential for $d\lambda/dN=0$). These specialized dynamical systems are too special if one hopes to distinguish the fixed points that 