7.1.8 (A circular limit cycle) Consider x tax(x2 + x2 -1) + x =0, where a > 0. a) Find and classify all the fixed points. b) Show that the system has a circular limit cycle, and find its amplitude and period. c Determine the stability of the limit cycle. d) Give an argument which shows that the limit cycle is unique, i.e., there are no other periodic trajectories