Consider the following nonlinear system: Which of these statements is true? Select all that apply. A) There are no isolated closed trajectories for this system. B) For r 0, the corresponding solution trajectories spiral outward away from r = 1 in a counterclockwise fashion. C) For 0

Question

Consider the following nonlinear system:

Which of these statements is true? Select all that apply.
A) There are no isolated closed trajectories for this system. 
B) For r > 0, the corresponding solution trajectories spiral outward away from r = 1 in a counterclockwise fashion. 
C) For 0 < r < 1, the corresponding solution trajectories spiral toward the origin in a counterclockwise fashion. 
D) The unit circle is a semistable limit cycle. 
E) The unit circle is an unstable limit cycle.

Quizplus · Accepted Answer

The Answer of Consider the following nonlinear system:

Which of these statements is true? Select all that apply.
A) There are no isolated closed trajectories for this system. 
B) For r > 0, the corresponding solution trajectories spiral outward away from r = 1 in a counterclockwise fashion. 
C) For 0 < r < 1, the corresponding solution trajectories spiral toward the origin in a counterclockwise fashion. 
D) The unit circle is a semistable limit cycle. 
E) The unit circle is an unstable limit cycle.

Consider the Following Nonlinear System