1. The problem statement, all variables and given/known data Consider the system x''+ax'(x2+x'2-1)+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. 2. Relevant equations y = x' For fixed points: x'=0, y'=0. 3. The attempt at a solution Using y=x', the system becomes: x' = y y' = -ax'(x2+x'2-1)-x Using x' = 0 and y' = 0, 1 Fixed point exists at (0,0). I'm not sure where to go from here. The problem is in Chapter 7, section 1 of "Nonlinear Dynamics and Chaos" by Strogatz.