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Homework Help: Using Poincare Bendixson's Theorem to prove a periodic Orbit

  1. Apr 17, 2013 #1
    1. The problem statement, all variables and given/known data
    The System is
    [itex]x˙ = 2x -y - x(x^2+y^2)[/itex]
    [itex]y˙ = 5x - 2y(x^2+y^2)[/itex]

    Using a trapping region to show there is a periodic orbit

    2. Relevant equations
    Use Poincare Bendixson's Theroem

    3. The attempt at a solution
    I tried constructing 2 Lyapunov type functions to show that DV/dt>0 and DV/dt<0 which show that in one region the flow is going into one region while the other is going out of the region. I could show that there is a region where the flow goes in if I use [itex]V=x^2+(ay^2/2)[/itex] but I can't figure another function to use to show the flow leaves a subspace. Is there another way to attempt this question?
    Last edited: Apr 17, 2013
  2. jcsd
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