Results 1 to 3 of 3

Math Help - Phase Plane, real unequal eigenvalues of the same sign

  1. #1
    Newbie
    Joined
    Aug 2012
    From
    Norway
    Posts
    5

    Phase Plane, real unequal eigenvalues of the same sign

    I have the following eigenvalues: r_1 = 4, r_2 = 2, which gives me the eigenvectors v_1 = [1, 1] and v_2 = [1,3] for r_1 and r_2 respectively. How should I draw the phase plane for this? This gives me two vectors that both approach infinity when t -> infinity? I've tried to find an example problem that draws the phase plane for this with no success. If anyone could either explain and/or point me to an example with this type of eigenvalues/vectors then that would be great. Thanks. :-)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,974
    Thanks
    1121

    Re: Phase Plane, real unequal eigenvalues of the same sign

    First, draw the lines corresponding to the eigenvectors. If both eigenvectors are positive, this is a "source", if negative, a "sink". Every line through the equilibrium point is a solution. In order to show the difference in eigenvalues, one thing you can do is draw the lines denser (closer together) close to the eigenvector with larger eigenvalue, farther apart close to the eigenvector with smaller eigenvalue.
    Last edited by HallsofIvy; August 27th 2012 at 09:25 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2012
    From
    Norway
    Posts
    5

    Re: Phase Plane, real unequal eigenvalues of the same sign

    Quote Originally Posted by HallsofIvy View Post
    First, draw the lines corresponding to the eigenvectors. If both eigenvectors are positive, this is a "source", if negative, a "sink". Every line through the equilibrium point is a solution. In order to show the difference in eigenvalues, one thing you can do is draw the lines denser (closer together) close to the eigenvector with larger eigenvalue, farther apart close to the eigenvector with smaller eigenvalue.
    Thank you for the input. However what I don't know how to do is how to draw the actual solutions, i.e. the lines that are drawn between the eigenvectors. What does it look like? Do you know what I could search for to find an example of how to do this?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: April 26th 2012, 06:49 AM
  2. Nonlinear terms - Phase plane
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: February 24th 2011, 03:09 PM
  3. Eigenvectors for the Phase Plane of a Two-Dimensional Linear System
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: November 15th 2010, 01:44 AM
  4. Phase plane problem
    Posted in the Differential Equations Forum
    Replies: 7
    Last Post: June 10th 2010, 02:55 AM
  5. given potential function, how to sketch phase plane
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: May 11th 2008, 12:57 PM

Search Tags


/mathhelpforum @mathhelpforum