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Question on nonlinear dynamics

  1. Mar 19, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider the system x' + x = F(t), where F is smooth, T-periodic function. IS it true that the system necessarily has a stable T-periodic solution x(t)? If so, Prove it; If not, find an F that provides a counterexample.

    2. Relevant equations

    x' + x = F(t)


    3. The attempt at a solution

    So, I think this system necessarily have a T-periodic solution x(t). To prove it, I let y = t so i can eliminate the time parameter from the equation so then I get a 2D system

    x' = F(y) - x
    y' = 1

    SO, then I plan to find a poincare map so that showing that x(t) is T-periodic.

    MY question is, before I go further, is this a good approach to the problem?

    thanks.
     
  2. jcsd
  3. Mar 19, 2012 #2

    lanedance

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    Homework Helper

    could you consider a fourier expansion?
     
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