Originally Posted by

**monster** Cheers! helps heaps,

Have gone ahead and completed my original questing and calculated the stability of the fixed points,

I said that;

$\displaystyle

f(x) = rx - \frac{x}{1+x^2}

$

and then that the derivative;

$\displaystyle

f ' (x) = r - \frac{1-x^2}{(1+x^2)^2}

$

and i then substituted equation of fixed points in for x,

which gave a messy function of r which i simplified down to;

$\displaystyle

f ' (x_0) = 2r - 2r^2

$

Where $\displaystyle x_0$denotes fixed points.

And considering that the question stated r > 0

i figure that;

fixed points where 0 < r < 1 are unstable

fixed points where r > 1 are stable

and when r=1 fixed points inconclusive?

I hope i did all the algebra in between steps correctly, but have i gone about this the right way am trying to follow text book but a little hard to understand without examples.

Many thanks for help, is VERY helpful.