Slow manifold ($f(x,y)=0$)

For a fast-slow system $ϵ\dot{x}=f(x,y)$, $\dot{y}=g(x,y)$, the formal critical manifold is $f=0$. Where the fast linearization has eigenvalues with strictly negative real parts, trajectories rapidly approach a nearby attracting slow manifold and then evolve on the slow time. Near folds or loss of this spectral condition, simply imposing $f=0$ may fail.