The sequence of behavior should now be apparent. As we have seen at a=3.498 we have a super stable 4-cycle, which corresponds to a superstable fixed point in f 4. We need only study the behavior in the region near x=½ given by scaling and truncating by putting nsc=2.
Increasing to a=3.545 the height of the curve goes up, the slope at the fixed point decrease below -1 and the fixed point goes unstable to a 2-cycle in f 4, i.e. an 8-cycle in f.
At a=3.5546 this becomes a super stable cycle:
shown as superstable fixed points in f 8=f 4(f 4(x))
We can focus on the central region be enlarging and inverting (increasing nsc to 3):
and we are back to the same situation as in the first applet except: