Chapter 5, Exploration 13

The graph below is not a tangent bifurcation. Animate the graph by dragging the slider from left to right to increase \(c\). Use is to answer the following questions.

  1. Identify the value of the parameter \(c\) where the graph is tangent to the line \(y=x.\)
  2. How many fixed points are there prior to this value of \(c\)? How many fixed points are there after this value of \(c\)? What are their stabilities?
  3. Draw the bifurcation diagram.
  4. Explain what the difference is between these graphs and the graph for exploration 11. Can you use a single mathematical computation to explain why these two animations are not tangent bifurcations?