When , a period doubling bifurcation occurs, and periodic points will emerge as seen in Figure 1.
For this case, solving (9) for x yields
So it can be seen that the value for at which this change in stability occurs can be "pushed off" simply by increasing . This can be seen in comparing Figure 2 to Figure 1. In Figure 2, the addition of the term has necessitated a larger value of in order for the onset of the period doubling bifurcation.