  In this work, we study a coupled system of two V-type atoms with
dipole-dipole interaction in a dissipative single-mode cavity, which couples
with an external environment. We obtain the analytical solution of this model
by solving the time dependent Schrodinger equation after we diagonalize
Hamiltonian of dissipative cavity by introducing a set of new creation and
annihilation operators according to Fano theorem. We also detailedly discuss
the influences of cavity-environment coupling, spontaneously generated
interference (SGI) parameter and dipole-dipole interaction between two atoms on
entanglement dynamics under different initial states. The results show that the
SGI parameter has different effects on entanglement dynamics under different
initial states. Namely, the SGI parameter will increase the decay rate of the
initially maximal entangled state and reduce that of the initially partial
entangled state. For the initially product state, the larger SGI parameter
corresponds to the more entanglement generated. The entanglement monotonically
decreases under the weak cavity-environment coupling, while the oscillation of
entanglement will occur under the strong cavity-environment coupling. The
larger the dipole-dipole interaction is, the slower the entanglement decays and
the more the entanglement will be generated. So the dipole-dipole interaction
can not only protect and generate entanglement very effectively, but also
enhance the regulation effect of the SGI parameter on entanglement.
