  It is shown that Einstein's field equations for \emph{all} perfect-fluid
$k=0$ FLRW cosmologies have the same form as the topological normal form of a
fold bifurcation. In particular, we assume that the cosmological constant is a
bifurcation parameter, and as such, fold bifurcation behaviour is shown to
occur in a neighbourhood of Minkowski spacetime in the phase space. We show
that as this cosmological constant parameter is varied, an expanding and
contracting de Sitter universe \emph{emerge} via this bifurcation.
