quantum effect, the dynamical system will be very different from the one in classical cosmology, e.g., the number of dimensions of autonomous system will change to four in LQC. It must be pointed out that this method cannot be used to describe the dynamical behavior of scalar field with arbitrary potential. To overcome this problem, therefore, we should consider an infinite-dimensional autonomous system.

The paper is organized as follows. In Sec. \[sec2\], we present the basic equations and the four dimensional dynamical system, and in Sec. \[sec3\], we discuss the properties of this system. In Sec. \[sec4\], we discuss the autonomous system in greater detail, as well as an infinite-dimensional autonomous system. We conclude the paper in the last section. The Appendix contains the analysis of the dynamical properties of one of the fixed points, $P_3$.

Basic equations {#sec2}
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We focus on the flat Friedmann-Robertson-Walker cosmology. The modified Friedmann equation in the effective LQC with holonomy correction can be written as [@Ashtekar-improve] $$\begin{aligned}
H^2=\frac{1}{3}\rho\left(1-\frac{\rho}{\rho_c}\right),\label{Fri}\end{aligned}$$ in which $\rho$ is the total energy density and the natural unit $\kappa=8\pi G=1$ is adopted for simplicity. We consider a self-interacting scalar field $\phi$ with a positive potential $V(\phi)$ coupled with a barotropic fluid. 