Global Bifurcation Map of the Homogeneous States in the Gray–Scott Model

We study the spatially homogeneous time-dependent solutions and their bifurcations in 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 bifurcation, in the space of two parameters k–F. With the aid of numerical continuation of local bifurcation curves we give a global description of all the possible bifurcations.