Consider the Following Nonlinear System Expressed in Polar Form

Multiple Choice

Consider the following nonlinear system expressed in polar form:
= r( r - 2) ( r - 8)
= 1
Which of these statements is true? Select all that apply.

A) r = 8 is a semistable limit cycle.
B) r = 2 is an asymptotically stable limit cycle.
C) For 2 < r < 8, the corresponding solution trajectories spiral outward away from r = 2 in a clockwise fashion.
D) For 0 < r < 2, the corresponding solution trajectories spiral toward the origin in a clockwise fashion.
E) For r > 8, the corresponding solution trajectories spiral outward away from r = 8 in a counterclockwise fashion.