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Homework Help: Draw phase protrait, the direction

  1. Jun 8, 2010 #1
    1. The problem statement, all variables and given/known data

    x' = y-x
    y' = (x-1)(y-2)

    Determin the the type of equilibriums

    2. Relevant equations

    I have found the equilibriums and that one of them is a sink.
    Eigenvalues (-1 +- sqrt(3))/2 with centre (1,1)

    Now can I just determin the direction by looking at (1,2), where x' = 2 and y' = 0 and say ot goes clockwise?

    Next question: I got two equilibrium points the sexond is in (2,2) and is a saddle.
    Are there any rule for how I should draw two equilibrium points? I mean they are very close.
  2. jcsd
  3. Jun 8, 2010 #2
    Yes, this is fine.

    Close is of course relative to how far you draw them apart. Anyway, keep in mind that to draw the saddle properly you will need to know the eigenvectors as well.
  4. Jun 9, 2010 #3
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