Now a is increased to 3.01. Hit "Start" to iterate the map, and occassionally clear the plot by hitting "Clear".
The orbit eventually ends up jumping back and forth between two values of x straddling the fixed point.
Starting the iteration near the fixed point:
leads to an orbit that gradually diverges from the fixed point, showing it to be unstable.
The second iterate of the map f 2(x) now has a slope slightly greater than unity at the original fixed point, and there are two additional intersections giving two new fixed points.