the stability characteristics of all periodic solutions

[anntara khan]

I am not sure how to analyze the stability around the limit circle. Is it dependent on the values of r or the value of r'(positive/negative)? And what does it really mean if it's Stable, Unstable or Semi-stable?

[Victor Ivrii]

Limit cycles (not circles) are not covered by final exam. In contrast to spiral point these cycles have two sides: external and internal. See picture