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 ,xxyyxy; (ii) 42 ,32xxyyxy (iii) 2,xxyyxy 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),2xxyyxyxy; (ii) 2,1xxyyxQ3. 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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Quadratic equation, Linear system, Nonlinear system, nonlinear systems, following linear systems