Differential Equations Phase Planes

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11 Terms

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Saddle Point

real eigenvalues of opposite sign

<p>real eigenvalues of opposite sign</p>
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Center

Purely imaginary eigenvalues

<p>Purely imaginary eigenvalues</p>
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Spiral Source

complex eigenvalues with positive real part

<p>complex eigenvalues with positive real part</p>
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Spiral Sink

complex eigenvalues with negative real part

<p>complex eigenvalues with negative real part</p>
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Parallel Lines

One eigen value equals 0 while the other is any real number

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Proper Nodal Source

A repeated positive real eigenvalue with two linearly independent eigenvectors

<p>A repeated positive real eigenvalue with two linearly independent eigenvectors</p>
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Proper Nodal Sink

A repeated negative real eigenvalue with two linearly independent eigenvectors

<p>A repeated negative real eigenvalue with two linearly independent eigenvectors</p>
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Improper Nodal Source (Distinct)

Distinct positive real eigenvalue without two linearly independent eigenvectors

<p>Distinct positive real eigenvalue without two linearly independent eigenvectors</p>
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Improper Nodal Source (Repeated)

Repeated positive real eigenvalue without two linearly independent eigenvectors

<p>Repeated positive real eigenvalue without two linearly independent eigenvectors</p>
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Improper Nodal Sink (Distinct)

Distinct negative real eigenvalue without two linearly independent eigenvectors

<p>Distinct negative real eigenvalue without two linearly independent eigenvectors</p>
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Improper Nodal Sink (Repeated)

Repeated negative real eigenvalue without two linearly independent eigenvectors

<p>Repeated negative real eigenvalue without two linearly independent eigenvectors</p>