Exam 1, phase portraits, diff eq

both positive unique real eigenvalues

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