Results 1 to 1 of 1

Thread: Jacobain and consequence on Dynamics.

  1. #1
    Ant is offline
    Apr 2008

    Jacobain and consequence on Dynamics.


    When given a 2nd order autonomous system of linear ODEs. In lecture we've investigated the stability of fixed point by computing the matrix of partial derivatives (the Jacobian) evaluating at the fixed points, finding eigenvalues. Then, we usually form a new matrix J* which takes various forms based on what the nature of the eigenvalue is (real distinct, real degenerate, complex). From this we can then investigate the stability of any fixed points.

    Unfortunately, this process was only covered as a revision (because it's material covered in previous courses). However, in previous courses the cases were simplified (for example the eigenvalues were never 0), but in this course that isn't the case. I'm having the most trouble in dealing with the stability when one eigenvalue is 0. (i think here that perhaps truncating to linear terms doesn't suffice)

    So I'm a little lost for material from which I can study and learn the theory.

    Could anyone recommend any books, online lecture notes or the like which cover this topic?

    Last edited by Ant; Mar 10th 2013 at 11:24 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [LOGIC] Consequence of A and not A
    Posted in the Advanced Math Topics Forum
    Replies: 9
    Last Post: Jul 18th 2012, 07:57 AM
  2. Not logical consequence (First-order logic)
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Oct 18th 2010, 07:07 AM
  3. Consequence relation
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: Jan 22nd 2009, 01:34 PM
  4. Cauchy Mean Value Theorem Consequence problem
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Nov 25th 2008, 01:14 PM
  5. consequence
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Nov 12th 2005, 05:22 PM

Search Tags

/mathhelpforum @mathhelpforum