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

Question

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.

Quizplus · Accepted Answer

The Answer of 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.

Consider the Following Nonlinear System Expressed in Polar Form