  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.
