Move the curve slightly down (while keeping the diagonal in the same place). How many equilibria are there now? What happens when you cobweb starting from a point at the right-hand edge of the figure?
Another peculiarity of an updating function that is tangent to the diagonal at an equilibrium is that slight changes in the graph can produce big changes in the number of equilibria. The following are based on Figure 3.1.10.

Updating function is tungent to diagonal 1.5 Half-stable equilibriun cobweb starting above equilibrium moves closer cobweb starting below equilibrium moves away 0.5 0 0 0.5 1.5 Initial value