Nodes

EA$

stable improper node

2 distinct real roots,

λ1, λ2 < 0

unstable improper node

2 distinct real roots,

λ1, λ2 > 0

unstable saddle point

2 distinct real roots,

λ1 < 0 < λ2

stable proper node

repeated roots with distinct eigenvectors

λ1 = λ2 < 0

unstable proper node

repeated roots with distinct eigenvectors

λ1 = λ2 > 0

stable improper node

repeated roots with only 1 eigenvector

λ1 = λ2 < 0

unstable improper node

repeated roots with only 1 eigenvector

λ1 = λ2 > 0

stable center point

pure imaginary complex conjugate roots

λ1 = λ2 = ± ai

stable spiral point

pure imaginary complex conjugate roots

λ1 = λ2 = a ± bi

a < 0

unstable spiral point

pure imaginary complex conjugate roots

λ1 = λ2 = a ± bi

a > 0

stable improper node

unstable improper node

stable proper node

unstable proper node

stable center point

unstable saddle point

stable spiral point

unstable spiral point