---
abstract: 'We discuss the stability properties of an autonomous system in loop quantum cosmology. The system is described by a self-interacting scalar field $\phi$ with positive potential $V$, coupled with a barotropic fluid in the Universe. With $\Gamma=VV''''/V''^2$ considered as a function of $\lambda=V''/V$, the autonomous system is extended from three dimensions to four dimensions. We find that the dynamic behaviors of a subset, not all, of the fixed points are independent of the form of the potential. Considering the higher-order derivatives of the potential, we get an infinite-dimensional autonomous system which can describe the dynamical behavior of the scalar field with more general potential. We find that there is just one scalar-field-dominated scaling solution in the loop quantum cosmology scenario.'
author:
- Kui Xiao
- 'Jian-Yang Zhu'
title: Stability analysis of an autonomous system in loop quantum cosmology
---

[^1]

Introduction
============

The scalar field plays an important role in modern cosmology. Indeed, scalar-field cosmological models are of great importance in the study of the early Universe, especially in the investigation of inflation. The dynamical properties of a scalar fields also make an interesting research topic for modern cosmological studies [@Copeland-IJMPD; @Coley-Book]. The dynamical behavior of scalar field 