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Unformatted text preview: will not tell you whether the solutions go clockwise or counterclockwise. If  + 1  < 1, then solutions near the equilibrium must spiral inward. Computing  + 1  can be a pain. You should always seek to 1. Identify the real and imaginary parts. 2. Compute  + 1  2 and simplify if possible. Also, if you can prove this theorem you can save yourself future computation troubles:  + 1  2 = ( a + 1) 2 + b 2 , and  + 1  2 = tr ( J ) + det ( J ) + 1 (Recall that tr ( J ) is the sum of the diagonal entries of J .) If  + 1  = 1, then solutions near the equilibrium will closely approximate closed loops, but closed loops are not guaranteed. If  + 1  > 1, then solutions near the equilibrium will spiral out. 2...
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This note was uploaded on 10/12/2011 for the course MATH 464 taught by Professor Dougbullock during the Fall '08 term at Boise State.
 Fall '08
 DougBullock
 Math, Eigenvectors, Vectors

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