  In this paper we study continuous parametrized families of dissipative flows,
which are those flows having a global attractor. The main motivation for this
study comes from the observation that, in general, global attractors are not
robust, in the sense that small perturbations of the flow can destroy their
globality. We give a necessary and sufficient condition for a global attractor
to be continued to a global attractor. We also study, using shape theoretical
methods and the Conley index, the bifurcation global to non-global.
