Nodes
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18 Terms
1
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stable improper node
2 distinct real roots,
λ1, λ2 < 0
λ1, λ2 < 0
2
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unstable improper node
2 distinct real roots,
λ1, λ2 > 0
λ1, λ2 > 0
3
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unstable saddle point
2 distinct real roots,
λ1 < 0 < λ2
λ1 < 0 < λ2
4
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stable proper node
repeated roots with distinct eigenvectors
λ1 = λ2 < 0
λ1 = λ2 < 0
5
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unstable proper node
repeated roots with distinct eigenvectors
λ1 = λ2 > 0
λ1 = λ2 > 0
6
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stable improper node
repeated roots with only 1 eigenvector
λ1 = λ2 < 0
λ1 = λ2 < 0
7
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unstable improper node
repeated roots with only 1 eigenvector
λ1 = λ2 > 0
λ1 = λ2 > 0
8
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stable center point
pure imaginary complex conjugate roots
λ1 = λ2 = ± ai
λ1 = λ2 = ± ai
9
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stable spiral point
pure imaginary complex conjugate roots
λ1 = λ2 = a ± bi
a < 0
λ1 = λ2 = a ± bi
a < 0
10
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unstable spiral point
pure imaginary complex conjugate roots
λ1 = λ2 = a ± bi
a > 0
λ1 = λ2 = a ± bi
a > 0
11
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stable improper node
12
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unstable improper node
13
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stable proper node
14
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unstable proper node
15
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stable center point
16
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unstable saddle point
17
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stable spiral point
18
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unstable spiral point
Note 
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