Unstable fixed point.help me U may find interesting

[shatranz]

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!

 

[neurocomp2003]

please show a diagram and the equation.

 

[shatranz]

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...