  We investigate the dynamical transition processes of an
Einstein-Maxwell-scalar gravitational system between two local ground states
and an excited state in the anti-de Sitter spacetime. From the linear
perturbation theory, only the excited state possesses a single unstable mode,
indicating the dynamical instability. Such an instability is associated with
the tachyonic instability due to the presence of an effective potential well
near the event horizon. From the nonlinear dynamics simulation, through the
scalar field accretion mechanism, the critical phenomena in the transition
process of the gravitational system between the two local ground states are
revealed. The threshold of the accretion strength indicates the existence of a
dynamical barrier in this transition process, which depends on the coupling
strength between the scalar and Maxwell fields. On the other hand, for the
unstable excited state, there exists a special kind of critical dynamics with a
zero threshold for the perturbation strength. The perturbations of different
signs push the gravitational system to fall into different local ground states.
Interestingly, in an extended parameter space, there exist specific parameters
such that the perturbations of non-zero amplitude fail to trigger the single
unstable mode of the excited state.
