A bifurcation diagram is used in studying attractors with respect to certain parameters. Attractors have variables that will change the structure and periodicity, and the bifurcation diagram shows this. For varying values of a in the Henon map (along the x-axis), the 500th-600th generations are mapped along the y-axis. You can see that for the values of a such as 1 and 1.25, the Henon map is periodic, it oscillates through four different values. The other values of a produce a chaotic attractor.
