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Unformatted text preview: will not tell you whether the solutions go clockwise or counter-clockwise. 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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