Logistic equation graphs

 I found my model of the logistic equation and changed the factor r. This is r = 2.6. It settles quickly to a steady population.

Then I went for r=3.0. Now we clearly have oscillation between two population sizes.

Now r=3.5. There are 4 population sizes in the oscillation. We have passed another bifurcation point.

By r=3.9 there is no repeating pattern.

My numbers don't quite match those in the book I looked at but I've noticed that I started with x=0.1 and they started at x=0.2. I wonder if that makes a difference.