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Phase Portrait Eigenvalue Conditions
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Gravity
Terms in this set (12)
real, different λs
both > 0
repelling, unstable,
larger eigenvalue/vector pair dominates
nodal source
real, different λs
both < 0
attractive, stable
largest absolute value of eigenvalue/vector pair dominates
nodal sink
real, different λs
λ1 > 0 , λ2 < 0
saddle point
real, same λs
λ1 = λ2 > 0
2 eigenvectors
repelling
all pointing out
star node
real, same λs
λ1 = λ2 < 0
2 eigenvectors
stable
all pointing in
star node
real, same λs
λ1 = λ2 > 0
1 eigenvector
repelling, unstable
(straight line, pushes away from center)
degenerate node (horizontal line base)
real, same λs
λ1 = λ2 < 0
1 eigenvector
attractive, stable
(straight line, pulls toward center)
degenerate node
complex λ
real part = 0
marginally stable
rotating
concentric circles
center
complex λ
real part > 0
rotating, repelling
spiral outward
spiral source
complex λ
real part < 0
rotating, attractive
spiral inward
spiral sink
trace-determinant plane
critical parabola det(a)=tr(a)^2/4
det is y-axis, tr is x-axis
stability in trace-det plane
2nd quadrant, trA<0 and detA>0
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