  Major galaxy mergers can trigger nuclear activities and are responsible for
high-luminosity quasi-stellar objects /active galactic nuclei (QSOs/AGNs). In
certain circumstances, such mergers may cause dual active galactic nuclei
(dAGN) phenomenon. This study investigates dAGN triggering and evolution of
massive black holes (MBHs) during the merging processes using hydrodynamic code
GADGET-2 to simulate several gas-rich major mergers at redshift $z=2$ and $3$,
respectively. Results reveal that gas-rich major mergers can trigger
significant nuclear activities after the second and third pericentric passages
and the formation of dAGN with significant time duration ($\sim 10 - 390$ Myr).
During the merging processes, galactic bulge evolves with time because of the
rapid star formation in each (or both) galactic centers and initial mixing of
stars in galactic disks due to violent relaxation. MBHs grow substantially due
to accretion and finally merge into a bigger black hole. The growth of galactic
bulges and corresponding increases of its velocity dispersions predate the
growth of MBHs in the dAGN stages. The MBHs in these stages deviate below the
relation between MBH mass and bulge mass (or velocity dispersion), and they
revert to the relation after the final mergers due to the significant accretion
that occurs mostly at a separation less than a few kpc. Then, the two MBHs
merge with each other.
