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.