10. Consider the system 3 X = Axyxr2+/1, r x2 ) j.r =x -+ ,1}: _:)._,I,Z + ,1_35 T where 7 is the polar radius. Prove that this has a stable limit cycle when A > 0. (Hint: Transformation to polar coordinates will be useful; you should be able to find an annulus that is guaranteed to contain a limit cycle.) Plot some orbits numerically as A varies to verify your conclusions