Self accelerating solutions in a DGP brane with a scalar field trapped   on it: the dynamical systems perspective
  We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped on a DGP brane. The simplest kinds of self-interaction potentials are investigated: a) constant potential, and b) exponential potential. It is shown that the dynamics of DGP models can be very rich and complex. One of the most interesting results of this study shows that dynamical screening of the scalar field self-interaction potential, occuring within the Minkowski cosmological phase of the DGP model and mimetizing 4D phantom behaviour, is an attractor solution for a constant self-interaction potential but not for the exponential one. In the latter case gravitational screening is not even a critical point of the corresponding autonomous system of ordinary differential equations. 
Israel Quiros, Ricardo Garcia-Salcedo, Tonatiuh Matos, Claudia Moreno