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Circular Limit Cycle

  1. Oct 20, 2008 #1
    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.
  2. jcsd
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