  We investigate the internal dynamics of the spinor Bose-Einstein Condensates
subject to dissipation by solving the Lindblad master equation. It is shown
that for the condensates without dissipation its dynamics always evolve along
specific orbital in the phase space of ($n_0$, $\theta$) and display three
kinds of dynamical properties including Josephson-like oscillation,
self-trapping-like oscillation and 'running phase'. In contrast, the
condensates subject to dissipation will not evolve along the specific dynamical
orbital. If component-1 and component-(-1) dissipate in different rates, the
magnetization $m$ will not conserve and the system transits between different
dynamical regions. The dynamical properties can be exhibited in the phase space
of ($n_0$, $\theta$, $m$).
