10 terms

Phase Portrait Eigenvalue Conditions

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real, different λs
both > 0
repelling, unstable,
larger eigenvalue/vector pair dominates
real, different λs
both < 0
attractive, stable
largest absolute value of eigenvalue/vector pair dominates
real, different λs
λ1 > 0 , λ2 < 0
saddle point
real, same λs
λ1 = λ2 > 0
2 eigenvectors
repelling
all pointing out
real, same λs
λ1 = λ2 < 0
2 eigenvectors
stable
all pointing in
real, same λs
λ1 = λ2 > 0
1 eigenvector
repelling, unstable
(straight line, pushes away from center)
real, same λs
λ1 = λ2 < 0
1 eigenvector
attractive, stable
(straight line, pulls toward center)
complex λ
real part = 0
marginally stable
rotating
concentric circles
complex λ
real part > 0
rotating, repelling
spiral outward
complex λ
real part < 0
rotating, attractive
spiral inward
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