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System of DEs

  1. Dec 14, 2011 #1
    I am confused on how to solve the following problem.

    Consider the system

    [itex]\vec{x}[/itex]t=A[itex]\vec{x}[/itex]+[itex]\vec{f}[/itex]

    where [itex]\vec{x}[/itex], [itex]\vec{f}[/itex] are vectors of size n and A is a
    constant nxn matrix. Characterize all matrices A so that for all periodic functions
    [itex]\vec{f}[/itex] (irrespective of period) there will be at most one periodic solution.

    I think we want no complex eigenvalues for the homogenous solution to have no
    periodic solutions, however am not sure and am lost with the forcing function.
     
  2. jcsd
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