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