Homework 9.3 Question 16

[Shengnan Li]

For Q16 on 9.3, phase portrait shows that xy tends toward a circle. I attached the picture below.
By definition of a critical point, I only found (0,0) but I feel like the circle related to 1-x^2-y^2 behaves similar as critical point.
How should I show that in the solution? Could anyone lead me with some procedure?
Thanks in advance.

[Victor Ivrii]

It is called Limiting Cycle. See section 9.6(?) which we did not study

[Shengnan Li]

while it's assigned as a question of section 9.3, are we supposed to analysis it somehow with some knowledge we learned without 9.7 information? or it's fine to omit it since we did not cover limit cycles?

[Victor Ivrii]

You don't need more advanced knowledge to get this right. In Final there will be no such questions