4 W 3 This Exercise Explores The Special Case Of A Two Dimensional Dynamical System Where One Of The Eigenvalues Satisfi 1 (17.85 KiB) Viewed 29 times
4 W 3 This Exercise Explores The Special Case Of A Two Dimensional Dynamical System Where One Of The Eigenvalues Satisfi 2 (37.92 KiB) Viewed 29 times
4.W.3 This exercise explores the special case of a two-dimensional dynamical system where one of the eigenvalues satisfies 11 = 1, and the other satisfies ( < 12 < 1. Sometimes these systems are referred to as stable combs.
a) First we consider the case of the diagonal matrix D below. Sketch the special trajectories and at least 6 others, with at least one trajectory in each quadrant. Write a sentence predicting what the trajectories will be in general (an educated guess is fine). 10 = 0 D-161 b) Now do the same for the matrix A below. Hint: The trajectories should be lines (not neces- sarily through the origin). Pay careful attention to the slope of the line. 1 A A-[57] 2
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