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Homework Help: Lorenz (stability with Liapunov function)

  1. Nov 30, 2008 #1


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    1. The problem statement, all variables and given/known data

    Using the Liapunov function [tex]V=1/2(x^2+\sigma y^2 + \sigma z^2)[/tex], obtain conditions on sigma, rho, beta sufficient for global asymptotic stability of the origin in the Lorenz equation.

    2. Relevant equations

    The Lorenz equation

    [tex]\dot{x}=\sigma (y-x); \dot{y}=\rho x-y-xz; \dot{z}=-\beta z + xy[/tex]

    3. The attempt at a solution

    [tex]\dot{V}=-\sigma (x^2+y^2+\beta z^2-(\rho+1)xy)[/tex]

    Now i have to find conditions on beta and rho such the term in the brackets is positive , at least locally around (0,0,0). But I don't really know how to do that.
  2. jcsd
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