For the system

linearise the system around the fixed point and comment on the stability properties for

The system can be written in polar coordinates as

By solving these equations, comment on the stability properties of the fixed point for

I've found the fixed point to be (0,0). I found that the fixed point is a centre, and so stable but not asymptotically stable for all a - but this seems to simple when the question specifically mentions

.

I've converted the equations to polar coords and solved to get

but don't know where to go from here to comment on stability.

Any help would be really appreciated