Student Questions

MAT370

• Q: I am really struggling on 3a, and 3c. Could you give me a hint or can we really go over this in class. I read the material and worked on it last night. Nothing seems to be clicking!

  A: Sorry to hear that you're struggling. Let's see if this hint helps: If you have a recurrence relation of the form

  

  then

  1. To find fixed points, you solve for solutions of the equation x=f(x).
  2. Suppose that one of the fixed points found is . To test for stability, check : if , then the points is stable; if >1, unstable; if =1, neutrally stable (and the graph and cobwebbing may make the case clear).
  3. To do the cobwebbing, you simply bounce between the graphs of f and the line y=x, and see where fate leads you!

  In example 3d, for example, the function f is

  

  We solved for two roots (and hence two fixed points), , and then tested the stability of each by visual inspection of the graph:

    
  Figure 1: Graphs of y=x and f(x) intersect in two points (at .1 and .2).
  

  We could also have tested their stability by computing :

  

  so (.1 is a stable fixed point), whereas (.2 is an unstable fixed point).

• About this document ...