autonomous system is extended from two dimensions to three dimensions in classical cosmology. They found that this method can help investigate many quintessence models with different potentials. The goal of this paper is to extend this method for studying the dynamical behavior of a scalar field with a general potential coupled with a barotropic fluid in LQC.

LQC [@Bojowald-Living; @Ashtekar-overview] is a canonical quantization of homogeneous spacetime based on the techniques used in loop quantum gravity (LQG) [@Rovelli-Book; @Thiemann-Book]. Owing to the homogeneity and isotropy of the spacetime, the phase space of LQC is simpler than that of LQG. For example, the connection is determined by a single parameter $c$ and the triad is determined by $p$. Recently, it has been shown that the loop quantum effects can be very well described by an effective modified Friedmann dynamics. Two corrections of the effective LQC are always considered: the inverse volume correction and the holonomy correction. These modifications lead to many interesting results: the big bang can be replaced by the big bounce [@Ashtekar], the singularity can be avoided [@Singh], the inflation can be more likely to occur (e.g., see [@Bojowald; @Germani-inflation; @Copeland-superinflation; @Ashtekar-inflation; @Corichi-measure]), and more. But the inverse volume 