  In this manuscript we use the dynamical system approach to study the linear
dynamics of a Randall-Sundrum braneworld model with a tachyon scalar field
confined to the brane. We recognize that the form of the tachyon potential
plays a significant role in the evolution of the universe. For the case of an
inverse square potential we find that one of our new variables, $\lambda$, is
constant. We obtain critical points of the system in this situation and
investigate their stability using the linear perturbation method. Then we turn
to a Gaussian potential in which $\lambda$ is not constant. Using the idea of
instantaneous critical points we study the behavior of the universe and its
possible fates. One of the interesting results of this manuscript is that our
universe will probably experience another phase transition from acceleration to
deceleration in the future.
