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Drawing phase portrait

  1. Sep 7, 2010 #1
    1. The problem statement, all variables and given/known data

    I want to draw a phase portrait from linearization of a nonlinear differential equation with eigenvalues l1 =1 and l2= -1.
    With equilibrium in (2,2)

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

    2. Relevant equations



    3. The attempt at a solution

    First I compute the eigenvectors v1 = [0;1] v2 = [1;2]
    I then draw v1 as a horizontal line through the point (2,2).
    I then check the direction of x' to left and to the right of (2,2). F.ex x = 0 y = 2, then x' = 2. x = 3, y = 2, then x' = -1. So the direction on both sides are against the (2,2)

    Then I draw v2. I draw a straight line through (2,2) and (3,4). and check the direction to the left and to the right of (2,2). x = 1, y = 0, then x' = -1 and y' = 0, something wrong hear?, x = 3, y = 4, x' = 1 and y = 4. So the direction on both sides are away from (2,2)

    Is this the right idea for drawing phase portraits?

    Edit: There are two equilibrium points. The second one is a spiral sink in (1,1) which goes clockwise
     
  2. jcsd
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