practice3(2) - Practice Exam 3 MAP 4305 1 Calculate eAt for...

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Practice Exam 3: MAP 4305 * 1. Calculate e At for A = 2 1 0 0 0 2 0 0 0 0 3 1 0 0 0 3 2. Verify that the region containing the origin and bounded by the line segments L 1 : y = x +6 , x [ - 3 , 0], L 2 : y = 6 , x [0 , 3], L 3 : x = 3 , y [ - 3 . 6], L 4 : y = x - 6 , x [0 , 3], L 5 : y = - 6 , x [ - 3 , 0], and L 6 : x = - 3 , y [ - 6 , 3] is a trapping region for the Van der Pol oscillator: ˙ x = y + x - x 3 / 3 ˙ y = - x Explain why this region contains a non-constant periodic solution. 3. Using Lyapunov’s direct method, establish the stability properties of the equilibrium at the origin of
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  • Summer '06
  • DeLeenheer
  • English-language films, Human mitochondrial DNA haplogroup, Human mtDNA haplogroups, der Pol oscillator, Patrick De Leenheer, non-constant periodic solution

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