I have two equations $\frac{dq}{dt}$= $Rq + K - 1$ and $\frac{dK}{dt}$=$ Nq + N$. Here, N and R are just constants so I was ignoring them and just assigning a certain arbitrary value. Solving nullclines for this gives me $q = (1-K)/r$ and $q=-1$. So both of them are going to intersect at the fourth quadrant.
My trouble right now is sketching the phase portrait for this. Are the two eigenvectors supposed to be the same as the two nullclines? I always thought eigenvectors are nullclines were more or less different ideas but is the point of intersection of the two nullcines the stable equilibrium path for this solution?