Chapter 9, Exploration 16

Let's more carefully explore the emergence of the period 3 window using the graphical analysis tool. You will want to manipulate the parameter \(a\) from about \(a=3.8\) to \(a=3.87\). Pay particular attention to what happens to the graph of \(y=F^3(x)\) as the period 3 orbit appears. Describe what caused the sudden emergence of this window. In particular, what bifurcation does this look like? You may wish to minimize the sidebar menu to see both graphs next to each other.