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

• – John B May 23 '16 at 21:45
• Thanks, but these questions are asking something different to mine. I am asking how we initially determine the flow. – anon May 23 '16 at 21:59