MA 366 Trace-Determinant Plane

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Last updated 12:24 AM on 10/19/26
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14 Terms

1
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2 distinct positive real eigenvalues

unstable node (source)

2
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2 distinct negative real eigenvalues

stable node (sink)

3
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real eigenvalues with opposite signs

unstable saddle point

4
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one 0, one positive eigenvalues

line of unstable equilibria

5
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one 0, one negative eigenvalue

line of stable equilibria

6
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0 eigenvalues

plane of equilibria

7
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repeated zero eigenvalues (defective system)

line of shear equilibria

8
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repeated positive eigenvalues (non-defective)

unstable proper node (star source)

9
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repeated positive eignvalues (defective)

unstable improper (defective) node

10
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repeated negative eigenvalues (non-defective)

stable proper node (star sink)

11
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repeated negative eigenvalues (defective)

stable improper (defective) node/sink

12
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purely imaginary eigenvalues

non-asymptotic center

13
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complex eigenvalues with positive real part

unstable spiral source

14
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complex eigenvalues with negative real part

stable spiral sink