The equilibrium points are defined
by :
hence the point
is clearly a solution.

Another solution of this system is
a point with *x=y=a*, that is the new system to solve is :

Hence, we find
and

For r<1 there is only one equilibrium
point * 0* because there no
solution for

For r>1 there is three equilibrium points

The Matlab calculation of the bifurcation gives, for s=10, b=2.66 and 0<r<30 :

The equivalent diagram for 0<r<5 :

The Matlab program used to calculate
this is situated here. For coming back to this part
of th report click on *Bifurcations and Stability* in the upper window.