  We study the spatially homogeneous time dependent solutions and their
bifurcations of the Gray-Scott model. We find the global map of bifurcations by
a combination of rigorous verification of the existence of Takens Bogdanov and
a Bautin bifurcations, in the space of two parameters k and F. With the aid of
numerical continuation of local bifurcation curves we give a global description
of all the possible bifurcations
