  The dynamical behavior of tachyon field with an inverse potential is
investigated in loop quantum cosmology. It reveals that the late time behavior
of tachyon field with this potential leads to a power-law expansion. In
addition, an additional barotropic perfect fluid with the adiabatic index
$0<\gamma<2$ is added, and the dynamical system is shown to be an autonomous
one. The stability of this autonomous system is discussed using phase plane
analysis. There exist up to five fixed points with only two of them possibly
stable. The two stable node (attractor) solutions are specified, and their
cosmological indications are discussed. For the tachyon dominated solution, the
further discussion is stretched to the possibility of considering tachyon field
as a combination of two parts which respectively behave like dark matter and
dark energy.
