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

Isobaric yield ratio difference between the 140 $A$ MeV $^{58, 64}$Ni + $^{9}$Be reactions studied by antisymmetric molecular dynamics model