 Fold delay

Near a nondegenerate fold point of a critical manifold crossed with nonzero slow speed, the local balance can be written $\epsilon \dot{x}=y-x^2$, $\dot{y}=-1$ up to nonzero scalings and higher-order terms. A time interval $T$ gives $y=O(T)$; balancing $x^2$ with $y$ gives $x=O(T^{1/2})$, and balancing $\epsilon x/T$ with $T$ gives $T=O({\epsilon }^{2/3})$, $x=O({\epsilon }^{1/3})$. This layer delays departure from the fold relative to an instantaneous singular jump. It differs from the order-$\epsilon$ fast motion away from the fold.