For an $\mathbb{R}^2$ dynamical system, I am wondering how I can proceed to plot the phase portrait of a saddle-node fixed point using only the nullclines. I know how to plot the phase portrait using the eigenvalues and eigenvectors. However, the nullclines are usually faster to find.
Is it possible to infer anything about the stable and unstable manifold knowing only the nullclines and the vector field on them?