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Unformatted text preview: Make sure to provide a printout of the commands you used to generate the simulations and plots. [or your convenience, I have put a sample of a Mathematica notebook on the class webpage for a similar problem. To execute a command in Mathematica, you need to simultaneously press the shift and enter button.] 3. This problem considers the Van der Pol oscillator: x = x + yx 3 / 3 y =x Here ( x, y ) R 2 . Show that (0 , 0) is the only steady state, and that it is a repellor (linearization has two eigenvalues with positive real part). Show that the polytope { ( x, y ) R 2  x [3 , 3] , y [6 , 6] , y x + 6 , y x6 } is a trapping region. Conclude that the Van der Pol oscillator must have a periodic solution. * MAP 4484 / 5489; Instructor: Patrick De Leenheer. 1...
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 Summer '06
 DeLeenheer

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