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Unformatted text preview: b. Use Matlab to find the eigenvalues and eigenvectors for the linear approximation to (B*) about (0,0). Then, using the general solution to the system, prove your origin is a sink. 5. The seed is 2 a. Plot a few orbits of the corresponding linear system. They should appear to be circular about the origin. Prove this is indeed true. b. Use pplane to plot the system (C) in the interval |x,y|<2. c. Choose the smaller scale so that you can really see what’s happening around the origin. Use (C) to prove (***). How does it follow that the orbits move constantly toward the origin? How does the sign of the derivative function relate to the behavior of the function? How can you explain the fact that the computer shows you that the orbits are loops when in fact they are spirals? d. Use pplane to plot the specific orbit which starts at x = 0, y = -0.2, use the intervals |x,y|<3 and the zoom-in feature several times near the origin to approximate this radius....
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- Spring '11