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Homework4_2010 - ME 580 Nonlinear Systems Home Work No 4...

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ME 580 Nonlinear Systems Home Work No. 4 Due: October 21, 2010 Q1. Sketch the phase diagrams for the following linear systems and classify the equilibrium points. (i) 5 , x x y y x y ; (ii) 4 2 , 3 2 x x y y x y   (iii) 2 , x x y y x y    Q2. Locate and classify the equilibrium points of the following systems. Sketch the phase diagrams: it will be helpful to obtain isoclines and path directions at other points in the field. (i) , 2 x x y y x y xy ; (ii) 2 , 1 x x y y x Q3. Use Bendixson’s theorem to show that the response amplitudes a, b for the van der Pol equation in the ‘van der Pol’ plane described by the equations
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