 Fold point of a critical manifold

For one fast and one slow variable, a nondegenerate fold point of a critical manifold satisfies $F=F_x=0$ and $F_{xx}{F}_y\ne 0$. An attracting and a repelling branch of fast equilibria meet there. A slow trajectory reaching the fold generally leaves by a rapid jump when its slow drift crosses the fold transversely. The fold is defined relative to the fast direction: if fast trajectories are slanted in the plotted coordinates, their tangency to the critical manifold need not be an extremum of its plotted height.