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

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