Q:

Find the flow for the following dynamical system

I have the following dynamical system: 
$\dot{x_1}= -x_2 + (x_1(1-(x_1^2+x_2^2)^2))$ , $
\dot{x_2}= x_1 + (x_2(1-(x_1^2+x_2^2)^2))$, 
$\dot{x_3}= \epsilon x_3$ .
 I am required to work out the flow for this system. I have switched it to cylindrical coordinates obtaining $\dot{r}=r(1-r^4)$ , $\dot{\theta}=1$, $\dot{z}=\epsilon{z}$.
I assume in order to work out $r$ I must use partial fractions, but I'm not really sure how to proceed with this, as surely it gets a bit awkward. Have I made a mistake somewhere? Is this the right approach?
Thanks

A:

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