Chapter 9, Exploration 11
You know that an attracting period 2 orbit exists for \(a\) slightly bigger than 3 because we have shown that a period-doubling bifurcation occurs at \(a=3.\) Use the logistic bifurcation tool to answer the following questions.
- At approximately what value of \(a\) does the period 2 orbit bifurcate to a period 4 orbit?
- At approximately what value of \(a\) does the period 4 orbit bifurcate to a period 8 orbit?
- At approximately what value of \(a\) does the period 8 orbit bifurcate to a period 16 orbit?