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Unformatted text preview: â€¢ Î» will not tell you whether the solutions go clockwise or counterclockwise. â€¢ If  Î» + 1  < 1, then solutions near the equilibrium must spiral inward. â€¢ Computing  Î» + 1  can be a pain. You should always seek to 1. Identify the real and imaginary parts. 2. Compute  Î» + 1  2 and simplify if possible. Also, if you can prove this theorem you can save yourself future computation troubles:  Î» + 1  2 = ( a + 1) 2 + b 2 , and  Î» + 1  2 = tr ( J ) + det ( J ) + 1 (Recall that tr ( J ) is the sum of the diagonal entries of J .) â€¢ If  Î» + 1  = 1, then solutions near the equilibrium will closely approximate closed loops, but closed loops are not guaranteed. â€¢ If  Î» + 1  > 1, then solutions near the equilibrium will spiral out. 2...
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 Fall '08
 DougBullock
 Math, Equilibrium, Eigenvectors, Vectors, Eigenvalue, eigenvector and eigenspace, dominant eigenvalue, dominant eigenvector

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