Stability of fixed points
The eigenvalues of the fixed points
are:
fixed points 
and 
fixed point 
fixed point
For this fixed point we find the following condition:
The solution is
Global attraction
Ljapunov functions
Only if 
this condition is fulfilled.
The solutions are:
or 
.
The solution is: 
The inner fixpoint
For the location of the inner fixed point a longer calculation leads to
, 
and 
are easily given by inserting
A further result is obtained by equating
with 0, which is valid for every fixed point. On
top of the ridge 
is the same as 
, which can be transformed to
For the inner fixed point that leads to
For the analysis of stability the system of
differential equations is reduced by 
to two equations. The following dependency for the eigenvalues appears:
It can be demonstrated that 
.
This leads to
Because there is a positive and a negative eigenvalue the inner fixed point is a saddlepoint and therefore unstable.