Given the following dynamical system
$$\begin{aligned} \dot r &= r(1-r^2) \\ \dot \theta &= r^2 \left( (1-r^2)^2 + \sin(\theta)^2 \right)\end{aligned}$$
find the annulus $A$ defined as follows
$$A(R_+, R_-) = \{(x,y) \mid R_-^2 \le x^2+y^2 \le R_+^2\}$$
where this system is positively invariant.
My thinking was that for my annulus I would want $2$ circles $(R_-,R_+)$ and I by looking at the phase flow and thought that $R_-$ would need to be 1, but I also thought that R_+ must also be 1. I thought that because I need the phase flow to be pointing outwards of my smaller circle $R_-$ for it to be positively invariant, but I'd need the phase flow to be pointing inward for our bigger circle $R_+$ so this happens at $1$ too.
I don't think my attempt is correct, but it is what I was thinking.