Global bifurcation map of the homogeneus states in the Gray-Scott model

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