  The heavy-ion fusion reactions induced by neutron-rich nuclei are
investigated with the improved quantum molecular dynamics (ImQMD) model. With a
subtle consideration of the neutron skin thickness of nuclei and the symmetry
potential, the stability of nuclei and the fusion excitation functions of
heavy-ion fusion reactions $^{16}$O+$^{76}$Ge, $^{16}$O+$^{154}$Sm,
$^{40}$Ca+$^{96}$Zr and $^{132}$Sn+$^{40}$Ca are systematically studied. The
fusion cross sections of these reactions at energies around the Coulomb barrier
can be well reproduced by using the ImQMD model. The corresponding slope
parameter of the symmetry energy adopted in the calculations is $L \approx 78$
MeV and the surface energy coefficient is $g_{\rm sur}=18\pm 1.5$ MeVfm$^2$. In
addition, it is found that the surface-symmetry term significantly influences
the fusion cross sections of neutron-rich fusion systems. For sub-barrier
fusion, the dynamical fluctuations in the densities of the reaction partners
and the enhanced surface diffuseness at neck side result in the lowering of the
fusion barrier.
