Dynamical systems analysis of an interacting dark energy model in the brane scenario

In this paper, we investigate the background dynamics in brane cosmology when dark energy is coupled to dark matter by a suitable interaction. Here we consider an homogeneous and isotropic Friedmann–Robertson–Walker brane model and the evolution equations are reduced to an autonomous system by suitable transformation of variables. The nature of critical points are analyzed by evaluating the eigenvalues of linearized Jacobi matrix. Finally, the classical stability of the model is also studied.