 Critical manifold

For a system $\epsilon \dot{x}=F(x,y)$, $\dot{y}=G(x,y)$ with fast variable $x$ and slow variable $y$, the critical manifold is the set of equilibria of the fast problem $dx/ds=F(x,y)$ with $y$ frozen. It is attracting where the fast Jacobian matrix has eigenvalues with negative real parts and repelling where those real parts are positive. A smooth graph can cease to be attracting at a fold point of a critical manifold.