Exam 1, phase portraits, diff eq

both positive unique real eigenvalues

unstable nodal source

both negative unique real eigenvalues

asymptotically stable nodal sink

opposite signs real eigenvalues

unstable saddle

1 eigenvalue\=0, 1 \> 0 both real

draw line of critical points, points going out

1 eigenvalue\=0, 1 < 0 both real

draw line of critical points, going toward line

imaginary eigenvalues, constant < 0

asymptotically stable spiral sink (CCW)

imaginary eigenvalues, constant \> 0

unstable spiral source (CW)

imaginary eigenvalues, constant\=0

stable center (concentric circles)

repeated eigenvalues \> 0 DIAGONAL

unstable proper node

repeated eigenvalues < 0 DIAGONAL

asymptotically stable proper node

repeated eigenvalues \> 0, not diagonal

unstable improper node

repeated eigenvalues < 0, not diagonal

asymptotically stable improper node