next up previous
Next: Behavior of trajectories Up: Numerical analysis Previous: Numerical analysis

Behavior of fixed points

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 tex2html_wrap1603 , there will be three fixed points of the system. Xpp-Auto was used over a range of values of the parameter tex2html_wrap1603 to find the stability of the fixed points for those tex2html_wrap1603 values.

All fixed points were found to have 2 complex eigenvalues and 1 real eigenvalue for all values of tex2html_wrap1603 . This indicates that all solutions near the three fixed points will exhibit oscillatory behavior.

For values of tex2html_wrap1603 less than tex2html_wrap1665 there exist two unstable saddle fixed points and one stable fixed point which has a small positive tex2html_wrap1666 component and a small positive tex2html_wrap1667 component.

For values of tex2html_wrap1603 greater than tex2html_wrap1665 , all three fixed points are unstable saddle points, with one negative real eigenvalue and two complex eigenvalues with positive real parts.