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Unformatted text preview: 4. Consider a gradient system. Show that, away from ﬁxed points, the trajectories of the system cross the level sets of V at right angles, and that V is decreasing along the trajectories. 5. Consider the given by ¨ x + x = μ (1-x 2 ) ˙ x with μ > 0. Use Bendixson’s criterion to show that periodic solutions necessarily have to cross x = ± 1....
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This note was uploaded on 01/04/2012 for the course CDS 140b taught by Professor List during the Fall '10 term at Caltech.
- Fall '10