What the next series of plots shows is that as the parameter A is systematically increased from this first value of A = 2.5 to near 4, the behavior of the system changes very radically. Figure 2 shows periodic behavior at A = 3.25. (A=a)[On your calculator, the values you obtain will alternate between two values].


This time the size of  each generation alternates between two values.









Next we will observe what happens as the value of the parameter A is incresed even more.  This will be the period doubling route to chaos.