Braneworld cosmological solutions and their stability
  We consider cosmological solutions and their stability with respect to homogeneous and isotropic perturbations in the braneworld model with the scalar-curvature term in the action for the brane. Part of the results are similar to those obtained by Campos and Sopuerta for the Randall-Sundrum braneworld model. Specifically, the expanding de Sitter solution is an attractor, while the expanding Friedmann solution is a repeller. In the braneworld theory with the scalar-curvature term in the action for the brane, static solutions with matter satisfying the strong energy condition exist not only with closed spatial geometry but also with open and flat ones even in the case where the dark-radiation contribution is absent. In a certain range of parameters, static solutions are stable with respect to homogeneous and isotropic perturbations. 
Dmytro Iakubovskyi and Yuri Shtanov