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

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.