  We investigate the dynamics of a boundary field coupled to a bulk field with
a linear coupling in an anti-de Sitter bulk spacetime bounded by a Minkowski
(Randall-Sundrum) brane. An instability criterion for the coupled boundary and
bulk system is found. There exists a tachyonic bound state when the coupling is
above a critical value, determined by the masses of the brane and bulk fields
and AdS curvature scale. This bound state is normalizable and localised near
the brane, and leads to a tachonic instability of the system on large scales.
Below the critical coupling, there is no tachyonic state and no bound state.
Instead, we find quasi-normal modes which describe stable oscillations, but
with a finite decay time. Only if the coupling is tuned to the critical value
does there exist a massless stable bound state, as in the case of zero coupling
for massless fields. We discuss the relation to gravitational perturbations in
the Randall-Sundrum brane-world.
