  \item[Background] The isobaric yield ratio difference (IBD) method is found
to be sensitive to the density difference of neutron-rich nucleus induced
reaction around the Fermi energy. \item[Purpose] An investigation is performed
to study the IBD results in the transport model. \item[Methods] The
antisymmetric molecular dynamics (AMD) model plus the sequential decay model
GEMINI are adopted to simulate the 140$A$ MeV $^{58, 64}$Ni + $^{9}$Be
reactions. A relative small coalescence radius R$_c =$ 2.5 fm is used for the
phase space at $t =$ 500 fm/c to form the hot fragment. Two limitations on the
impact parameter ($b1 = 0 - 2$ fm and $b2 = 0 - 9$ fm) are used to study the
effect of central collisions in IBD. \item[Results] The isobaric yield ratios
(IYRs) for the large--$A$ fragments are found to be suppressed in the symmetric
reaction. The IBD results for fragments with neutron-excess $I = $ 0 and 1 are
obtained. A small difference is found in the IBDs with the $b1$ and $b2$
limitations in the AMD simulated reactions. The IBD with $b1$ and $b2$ are
quite similar in the AMD + GEMINI simulated reactions. \item[Conclusions] The
IBDs for the $I =$ 0 and 1 chains are mainly determined by the central
collisions, which reflects the nuclear density in the core region of the
reaction system. The increasing part of the IBD distribution is found due to
the difference between the densities in the peripheral collisions of the
reactions. The sequential decay process influences the IBD results. The AMD +
GEMINI simulation can better reproduce the experimental IBDs than the AMD
simulation.
