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In this manuscript we use the dynamical system approach to study the lineardynamics of a Randall-Sundrum braneworld model with a tachyon scalar fieldconfined to the brane. We recognize that the form of the tachyon potentialplays a significant role in the evolution of the universe. For the case of aninverse square potential we find that one of our new variables, $\lambda$, isconstant. We obtain critical points of the system in this situation andinvestigate their stability using the linear perturbation method. Then we turnto a Gaussian potential in which $\lambda$ is not constant. Using the idea ofinstantaneous critical points we study the behavior of the universe and itspossible fates. One of the interesting results of this manuscript is that ouruniverse will probably experience another phase transition from acceleration todeceleration in the future.

Dynamical System Analysis of Randall-Sundrum Model with Tachyon Field on the Brane