Solving equation (2.10) for x we find two period one
solutions,
and
The first period one orbit, labeled
,
always remains at the origin, while the location of the second period one orbit,
, depends on
. From equation (2.12), the stability of each of
these orbits is determined from
and
Clearly, if
then
and
, so
the period one orbit
is stable and
is unstable. At
these two orbits collide and exchange stability so that for
,
is unstable and
is stable. For
, both orbits are unstable.