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Unstable fixed point.help me U may find interesting

  1. Jul 21, 2006 #1
    Unstable fixed point..........help me!!!...U may find interesting!!!

    Dear friends,

    I have a 3-D non-linear equation. I have inearised it to get a single fixed point which turns out to be a repelling spiral (one +ve real eigenvalue, and two complex conjugates with +ve real part).....Now, the problem is whatever initial point (even if the initial point is very close to the fixed point itself, not to talk of the far of initial conditions) I take in the phase space and run 4th order runge-kutta code, the trajectory converges to the fixed point.....why should it be?..(To me it seems strange as the fixed point is repelling spiral!!!).....Please help me!!!
  2. jcsd
  3. Jul 21, 2006 #2
    please show a diagram and the equation.
  4. Jul 21, 2006 #3
    The equation is of the following type:

    dx/dt=-a*sqrt(x^2+y^2+z^2)*x - y*c*cos(alpha)
    dy/dt=-a*sqrt(x^2+y^2+z^2)*y + x*c*cos(alpha)+z*c*sin(alpha)
    dz/dt=-a*sqrt(x^2+y^2+z^2)*z - y*c*sin(alpha)-b

    where a,b,c,alpha are constants.......all positive

    I don't have the diagram right now.........but in whatever octant u take a point as the initial condition then for a=0.027, b=10, c=0.16, alpha=0.5 , all trajectories seem to reach a repelling spiral at about (0.7,-2.4,-18.8).......which has been calculated using linearisation technique.......
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