The behavior of the fixed points of this system were analyzed
numerically with Xpp-Auto, which calculates
numerically the eigenvalues of a fixed point. Figure [8(a)]
indicates that for a given value of , there
will be three fixed points of the system. Xpp-Auto was used over
a range of values of the parameter
to find the stability of the fixed points for those
values.
All fixed points were found to have 2 complex eigenvalues and 1 real
eigenvalue for all values of . This
indicates that all solutions near the three fixed points will exhibit
oscillatory behavior.
For values of less than
there exist two
unstable saddle fixed points and one stable
fixed point which has a small positive
component and a small
positive
component.
For values of greater than
, all three fixed
points are unstable saddle points, with
one negative real eigenvalue and two complex eigenvalues with positive real
parts.