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1

both positive unique real eigenvalues

unstable nodal source

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2

both negative unique real eigenvalues

asymptotically stable nodal sink

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3

opposite signs real eigenvalues

unstable saddle

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4

1 eigenvalue=0, 1 > 0 both real

draw line of critical points, points going out

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5

1 eigenvalue=0, 1 < 0 both real

draw line of critical points, going toward line

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6

imaginary eigenvalues, constant < 0

asymptotically stable spiral sink (CCW)

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7

imaginary eigenvalues, constant > 0

unstable spiral source (CW)

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8

imaginary eigenvalues, constant=0

stable center (concentric circles)

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9

repeated eigenvalues > 0 DIAGONAL

unstable proper node

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10

repeated eigenvalues < 0 DIAGONAL

asymptotically stable proper node

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11

repeated eigenvalues > 0, not diagonal

unstable improper node

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12

repeated eigenvalues < 0, not diagonal

asymptotically stable improper node

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