I know I need to convert it to polar system but I don't know how to do this
My system is
$$\dfrac{dx}{dt}= x - y -x(x^2 + 2y^2)$$
and
$$\dfrac{dy}{dt} = x + y -y(x^2 + y^2).$$
The annular region is $\frac{2}{\sqrt{5}} < r < 1$, which gives the polar system
$$
\begin{cases}
\dfrac{dr}{dt} = r - r^3 \left(1 + \frac{1}{4}\sin^2(2\theta)\right) \\
\dfrac{d\theta}{dt} = \left(1 + \frac{1}{2}r^2\sin(2\theta) - sin^2(\theta) \right)
\end{cases}
$$