Information Technology Reference
In-Depth Information
x D x
2
.
Converging arrows
denote
Fig. 2.17
Phase diagram and fixed points of the system
a stable fixed point
Fig. 2.18
Saddle-node bifurcation diagram
2.5.3
Pitchfork Bifurcation of Fixed Points
In pitchfork bifurcations the number of fixed points varies with respect to the values
of the bifurcation parameter. The dynamical system x D x. x
2
/ is considered.
The associated fixed points are found by the condition x D 0.For<0there is
one fixed point at zero which is stable. For D 0 there is still one fixed point at
zero which is still stable. For >0there are three fixed points, one at x D 0,
