Open one of the computer algebra systems below to follow along with this module. You may recall one of the logistic models we looked at. This kind of pattern in which the same numbers repeat over and over again is called a cycle. In this case because two numbers are repeating it is called a 2-cycle. When the repeating pattern has three numbers, it is called a 3-cycle and so forth.
Cycles have some similarities with equilibrium points.
Notice that equilibrium points are also a solution of this equation. In fact, there is no apparent pattern at all. This situation is called chaos. This is an open-ended assignment. Find as many examples as you can of cycles of different periods.