Let M= 
be the first intersection point
between the locus 
and
.
Then the system has a periodic solution with
frequency 
.
Moreover, let 
be the value such that 
. This value is associated with the
amplitude of the periodic orbit
so that the amplitude of 
, 
(defined in
figure 3)
and 
can be derived very
simply from .
Consider now the point 
, where
the positive number 
can
be chosen as small as needed to insure that
the vector 
has no other intersection with
than M.
If is encircled
anticlockwise by the loci of the eigenvalues a number of
times equal to the number of poles with positive real part of the corresponding
, the periodic orbit is an attractor.