The location and stability of the two period one orbits and the single period two orbit are summarized in the orbit stability diagram shown in Figure 2.13.
Figure 2.13: Orbit stability diagram.
The
vertical axis shows the location of the periodic
orbit 
as a function
of the parameter 
. Stable orbits are
denoted by solid lines, unstable orbits by dashed lines. Two
``bifurcation points'' are evident in the diagram.
The first occurs when
the two period one orbits collide and exchange
stability at 
. The
second occurs with the birth of a stable
period two orbit from a stable
period one orbit at 
.