MAT244-2013S > Quiz 4

Quiz 4--Problem (night sections)

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Victor Lam:
We got saddle points (unstable) for both (0,0) and (-2,0). Also (-1,-1) and (2,2) are both asymptotically stable spirals of clockwise orientation. Solutions can be seen in the visual.
Note as t approaches infinity, all points satisfying x > -2 ultimately approach the particular critical points.

Victor Lam:
Also, the line y = 0 is not included in the basin of attraction, as we look at the original system for dy/dt, there clearly is a y term there, which will just stay on the line y = 0. Hence, the basin of attraction for the two critical points can be represented by the 2 rectangles (one above y = 0, the other below y = 0).