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evaluating locally linear systems (stability, type, phase portrait)

Georgie D'Sanson Mathematics English 10 cards

evaluating locally linear systems (stability, type, phase portrait)

Cards in this deck (10)

  1. 1r1 < 0 < r2 (real and distinct eigenvalues r1, r2)r1 &lt; 0 &lt; r2 (real and distinct eigenvalues r1, r2)
  2. 20 < r1 < r2 (real and distinct eigenvalues r1, r2)nodal source0 &lt; r1 &lt; r2 (real and distinct eigenvalues r1, r2)
  3. 3r1 < r2 < 0 (real and distinct eigenvalues r1, r2)nodal sinkr1 &lt; r2 &lt; 0 (real and distinct eigenvalues r1, r2)
  4. 4λ = 0 (r1,r2 are complex conjugates r1 = λ + iμ)λ = 0 (r1,r2 are complex conjugates r1 = λ + iμ)
  5. 5λ > 0 (r1,r2 are complex conjugates r1 = λ + iμ)spiral sourceλ &gt; 0 (r1,r2 are complex conjugates r1 = λ + iμ)
  6. 6λ < 0 (r1,r2 are complex conjugates r1 = λ + iμ)spiral sinkλ &lt; 0 (r1,r2 are complex conjugates r1 = λ + iμ)
  7. 7r > 0 (r1 = r2, 1 linearly independent eigenvector)(source)r &gt; 0 (r1 = r2, 1 linearly independent eigenvector)
  8. 8r < 0 (r1 = r2, 1 linearly independent eigenvector)(sink)r &lt; 0 (r1 = r2, 1 linearly independent eigenvector)
  9. 9r > 0 (r1 = r2, 2 linearly independent eigenvectors)star node (source)
    unstable    r &gt; 0 (r1 = r2, 2 linearly independent eigenvectors)
  10. 10r < 0 (r1 = r2, 2 linearly independent eigenvectors)star node (sink)
    asymptotically stable    r &lt; 0 (r1 = r2, 2 linearly independent eigenvectors)

Information

Description
We want to solve x' = Ax. If detA =/= 0, then the origin is the only critical point. The following are different classifications of the zero vector for type and stability with corresponding phase portraits.
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